[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/16822#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/16822","headline":"\u30ab\u30bf\u30ed\u30cb\u30a2\u30b6\u30fc\u30eb – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2","name":"\u30ab\u30bf\u30ed\u30cb\u30a2\u30b6\u30fc\u30eb – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2","description":"before-content-x4 \u30ab\u30bf\u30ed\u30cb\u30a2\u306e\u6570\u5b57\u306f\u3001\u305f\u3068\u3048\u3070\u3001\u6570\u91cf\u306e\u975e\u4ea4\u914d\u30d1\u30fc\u30c6\u30a3\u30b7\u30e7\u30f3\u3092\u30ab\u30a6\u30f3\u30c8\u3057\u307e\u3059 n {displaystyle n} \u8981\u7d20\u3001\u3053\u3061\u3089 C5= 42 {displaystyle c_ {5} = 42} after-content-x4 \uff08\u4e0a\u8a18\uff09\u3001\u3053\u308c\u306b\u3088\u308a\u3059\u3079\u3066\u306e\u30d1\u30fc\u30c6\u30a3\u30b7\u30e7\u30f3\u304c\u30d9\u30eb\u30a2\u30f3\u306e\u4eba\u7269\u306b\u3088\u3063\u3066\u6307\u5b9a\u3055\u308c\u3066\u3044\u307e\u3059\u3002 after-content-x4 B5= 52 {displaystyle b_","datePublished":"2023-05-15","dateModified":"2023-05-15","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/e\/e7\/Noncrossing_partitions_5.svg\/220px-Noncrossing_partitions_5.svg.png","url":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/e\/e7\/Noncrossing_partitions_5.svg\/220px-Noncrossing_partitions_5.svg.png","height":"467","width":"220"},"url":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/16822","wordCount":11589,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4 \u30ab\u30bf\u30ed\u30cb\u30a2\u306e\u6570\u5b57\u306f\u3001\u305f\u3068\u3048\u3070\u3001\u6570\u91cf\u306e\u975e\u4ea4\u914d\u30d1\u30fc\u30c6\u30a3\u30b7\u30e7\u30f3\u3092\u30ab\u30a6\u30f3\u30c8\u3057\u307e\u3059 n {displaystyle n} \u8981\u7d20\u3001\u3053\u3061\u3089 C5= 42 {displaystyle c_ {5} = 42}        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\uff08\u4e0a\u8a18\uff09\u3001\u3053\u308c\u306b\u3088\u308a\u3059\u3079\u3066\u306e\u30d1\u30fc\u30c6\u30a3\u30b7\u30e7\u30f3\u304c\u30d9\u30eb\u30a2\u30f3\u306e\u4eba\u7269\u306b\u3088\u3063\u3066\u6307\u5b9a\u3055\u308c\u3066\u3044\u307e\u3059\u3002        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4B5= 52 {displaystyle b_ {5} = 52}  \u30ab\u30bf\u30ed\u30cb\u30a2\u306e\u6570 \u307e\u305f \u30ab\u30bf\u30ed\u30cb\u30a2\u306e\u6570 \u7d44\u307f\u5408\u308f\u305b\u306e\u591a\u304f\u306e\u554f\u984c\u3067\u767a\u751f\u3059\u308b\u81ea\u7136\u6570\u306e\u7d50\u679c\u3092\u5f62\u6210\u3057\u3001\u4e8c\u9805\u4fc2\u6570\u307e\u305f\u306f\u30d5\u30a3\u30dc\u30ca\u30c3\u30c1\u6570\u3068\u540c\u69d8\u306b\u91cd\u8981\u306a\u5f79\u5272\u3092\u679c\u305f\u3057\u307e\u3059\u3002\u5f7c\u3089\u306f\u3001\u30d9\u30eb\u30ae\u30fc\u306e\u6570\u5b66\u8005\u306e\u30aa\u30a4\u30b2\u30fc\u30cc\u30fb\u30c1\u30e3\u30fc\u30eb\u30ba\u30fb\u30ab\u30bf\u30ed\u30cb\u30a2\u8a9e\u306b\u3061\u306a\u3093\u3067\u540d\u4ed8\u3051\u3089\u308c\u307e\u3057\u305f\u3002 \u30ab\u30bf\u30ed\u30cb\u30a2\u306e\u6570\u306e\u7d50\u679c c 0 \u3001 c \u521d\u3081 \u3001 c 2 \u3001 c 3 \u3001 … {displaystyle c_ {0}\u3001c_ {1}\u3001c_ {2}\u3001c_ {3}\u3001dotsc} \u304b\u3089\u59cb\u307e\u308a\u307e\u3059 1\u30011\u30012\u30015\u300114\u300142\u3001132\u3001429\u30011430\u30014862\u300116796\u300158786\u3001208012\u3001742900\u3001… A000108 OEIS\u3067\uff09 \u30ab\u30bf\u30ed\u30cb\u30a2\u306e\u6570\u306f\u5411\u3051\u3089\u308c\u3066\u3044\u307e\u3059        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4n \u2265 0 {displaystyle ngeq 0} \u306b\u3088\u3063\u3066\u4e0e\u3048\u3089\u308c\u305f c n= 1n+1(2nn)= (2n)!(n+1)!n!\u3001 {displaystyle c_ {n} = {frac {1} {n+1}} {binom {2n} {n} {n}} = {frac {\uff082n\uff09\uff01} {\uff08n+1\uff09\uff01\u3001n\uff01}}\u3001}\u3001} \u3057\u305f\u304c\u3063\u3066 (2nn){displaystyle {tbinom {2n} {n}}} \u4e2d\u592e\u306e\u4e8c\u9805\u4fc2\u6570\u306f\u3067\u3059\u3002\u3068 (2nn+1)= nn+1(2nn){displaystyle {tbinom {2n} {n+1}} = {tfraac {n} {n+1}} {tbinom {2n} {n}}}}} \u306b\u76f8\u5f53\u3059\u308b\u5f0f\u3092\u53d6\u5f97\u3057\u305f\u5834\u5408 c n= (2nn) –  (2nn+1)MM Slavetle State \u2014 Happix 2 Refinee MJoy 2 repparent M H repparents MJoy 1 1-1\u89aaMJoy 1 1-1 \u3057\u305f\u304c\u3063\u3066\u3001\u5b9f\u969b\u306b\u306f\u6574\u6570\u306e\u307f\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002 \u4e2d\u56fd\u306e\u30df\u30f3\u30ac\u30c8\u30a5\u30ab\u30bf\u30ed\u30cb\u30a2\u4eba\u306e\u4eba\u7269\u306f\u3001\u4e09\u89d2\u95a2\u6570\uff081730\u5e74\u4ee3\u3068\u3057\u3066\u306e1730\u5e74\u4ee3\uff09\u306e\u7121\u9650\u306e\u5217\u3092\u6700\u521d\u306b\u898b\u3064\u3051\u307e\u3057\u305f\u304c\u30011839\u5e74\u306b\u306f\u672c\u3068\u3057\u3066\u306e\u307f\u51fa\u7248\u3055\u308c\u307e\u3057\u305f\uff09\u3002 \u3053\u306e\u30a8\u30d4\u30bd\u30fc\u30c9\u306e\u6570\u5b57\u306f\u30011751\u5e74\u306b\u30ad\u30ea\u30b9\u30c8\u6559\u306e\u30b4\u30fc\u30eb\u30c9\u30d0\u30c3\u30cf\u3078\u306e\u624b\u7d19\u3067\u30ec\u30aa\u30f3\u30cf\u30eb\u30c8\u30fb\u30aa\u30a4\u30e9\u30fc\u306b\u3088\u3063\u3066\u3059\u3067\u306b\u8aac\u660e\u3055\u308c\u3066\u3044\u307e\u3057\u305f\u3002 [\u521d\u3081] \u30e8\u30cf\u30f3\u30fb\u30a2\u30f3\u30c9\u30ec\u30a2\u30b9\u30fb\u30d5\u30a9\u30f3\u30fb\u30bb\u30b0\u30ca\u30fc\u306f1758\u5e74\u306b\u63a7\u8a34\u5f0f\u3092\u898b\u3064\u3051\u307e\u3057\u305f\u3002 [2] \u30bb\u30b0\u30ca\u30fc\u306e\u8a18\u4e8b\u306e\u8981\u7d04\u306b\u304a\u3051\u308b\u30aa\u30a4\u30e9\u30fc\u306e\u89e3\u6c7a\u7b56\u3002 [3] Johann Friedrich Pfaff\u304c\u4f5c\u6210\u3057\u305f\u3088\u308a\u4e00\u822c\u7684\u306a\u30ab\u30a6\u30f3\u30c8\u30bf\u30b9\u30af\u306f\u30011795\u5e74\u306e\u30cb\u30b3\u30e9\u30a6\u30b9\u30d5\u30a1\u30b9\u3092\u89e3\u6c7a\u3057\u307e\u3057\u305f\u3002 [4] 1838\u5e74\u30681839\u5e74\u306e\u30ac\u30d6\u30ea\u30a8\u30eb\u30e9\u30e1\u3001 [5] \u30aa\u30ea\u30f3\u30c9\u30fb\u30ed\u30c9\u30ea\u30b2\u30b9\u3001 [6] \u30b8\u30e3\u30c3\u30af\u30fb\u30d3\u30cd\u30c3\u30c8 [7] [8] eug\u00e8neCatalan [9] [\u5341] \u518d\u3073\u8cea\u554f\u3002 Eugen Netto\u306f1901\u5e74\u306b\u516c\u958b\u3055\u308c\u305f\u5f7c\u306e\u30ea\u30fc\u30c9\u3092\u7387\u3044\u307e\u3057\u305f \u7d44\u307f\u5408\u308f\u305b\u306e\u6559\u79d1\u66f8 \u30ab\u30bf\u30ed\u30cb\u30a2\u8a9e\u306e\u6570\u5b57\u3002 [11] \u30aa\u30a4\u30e9\u30fc\u306f\u53ef\u80fd\u6027\u306e\u6570\u3001\u51f8\u9762\u3092\u63a2\u3057\u3066\u3044\u307e\u3057\u305f n {displaystyle n}  – \u5bfe\u89d2\u7dda\u3092\u5207\u308a\u629c\u3051\u3066\u4e09\u89d2\u5f62\uff08\u4e09\u89d2\u6e2c\u91cf\uff09\u306b\u30ab\u30c3\u30c8\u3057\u307e\u3059\u3002\u3053\u306e\u756a\u53f7\u306f\u3067\u3059 c n  –  2 {displaystyle c_ {n-2}} \u3002\u305f\u3068\u3048\u3070\u3001\u4e94\u89d2\u5f62\u306b\u306f5\u3064\u306e\u53ef\u80fd\u306a\u4e09\u89d2\u6e2c\u91cf\u304c\u3042\u308a\u307e\u3059\u3002 1751\u5e74\u306e\u30b4\u30fc\u30eb\u30c9\u30d0\u30c3\u30cf\u3078\u306e\u624b\u7d19\uff08\u6b74\u53f2\u3092\u53c2\u7167\uff09\u3067\u3001\u30aa\u30a4\u30e9\u30fc\u306f\u660e\u793a\u7684\u306a\u516c\u5f0f\u3092\u4e0e\u3048\u307e\u3057\u305f Cn=2\u22c56\u22c510\u22ef(4n\u22122)2\u22c53\u22c54\u22ef(n+1)=\u220fk=1n4k\u22122k+1{displaystyle c_ {n} = {frac {2cdot 6cdot 10dotsb\uff084n-2\uff09} {2cdot 3cdot 4dotsb\uff08n+1\uff09}} = prod _ {k = 1}^{n} {frac {4k-2} {k+1}}}}}  \uff08*\uff09  \u3068\u5f0f \u2211 n=0\u221ec n\u30d0\u30c4 n= 1\u22121\u22124x2x= 21+1\u22124x{displaystyle sum _ {n = 0}^{infty} c_ {n} x^{n} = {frac {1- {sqrt {1-4x}}} {2x}} = {frac {2} {1+ {sqrt {1-4x}}}}}}}}} \u7279\u306b\u751f\u6210\u95a2\u6570\u306e\u5834\u5408 \u2211 n=0\u221eCn4n= 2 {displaystyle sum _ {n = 0}^{infty} {frac {c_ {n}} {4^{n}}} = 2} \u6210\u9577\u884c\u52d5\u306e\u8aac\u660e\u3068\u3057\u3066\u3082\u3002 [\u521d\u3081] \u30ac\u30f3\u30de\u95a2\u6570\u3067 c {displaystyle\u30ac\u30f3\u30de} \u8a72\u5f53\u3059\u308b\uff1a c n= 4n\u0393(12+n)\u03c0\u0393(2+n){displaystyle c_ {n} = {frac {4^{n} gamma {left\uff08{tfrac {1} {2}}+nright\uff09}} {sqrt {pi}}\u3001gamma {left\uff082+night\uff09}}}}}}}} \u5f0f\u304b\u3089\u76f4\u63a5 \uff08*\uff09 \u7d9a\u304d\u307e\u3059 c n+1= 4n+2n+2c n\u3002 {displaystyle c_ {n+1} = {frac {4n+2} {n+2}}\u3001c_ {n}\u3002} \u518d\u5e30\u5f0f\u3082\u9069\u7528\u3055\u308c\u307e\u3059\uff08Segner 1758\uff09 [2] c n+1= \u2211 k=0nc kc n\u2212k\u3001 {displaystyle c_ {n+1} = sum _ {k = 0}^{n} c_ {k}\u3001c_ {n-k}\u3001} \u305f\u3068\u3048\u3070\u3001\u3067\u3059 c 3 = c 0 c 2 + c \u521d\u3081 c \u521d\u3081 + c 2 c 0 {displaystyle c_ {3} = c_ {0}\u3001c_ {2}+c_ {1}\u3001c_ {1}+c_ {2}\u3001c_ {0}} \u3002 \u5225\u306e\u518d\u5e30\u5f0f\u304c\u3042\u308a\u307e\u3059 c n+1= \u2211 k=0\u230an\/2\u230b(n2k)2 n\u22122kc kM TUME SLEXLE STATE EMPASUXM\u00e9ReporalKoror Horor M Hork2K\u00f62ok\uff09\u30de\u30eb\u30e1\u30a4\u30c8\u3001Saml\u0254\u307e\u305f\u306f22-25- Motzkin NumbersM\u3068\u540c\u69d8\u306bM\uff08\u30b7\u30fc\u30b1\u30f3\u30b9 A001006 OEIS\u3067\uff09 c n+1= \u2211 k=0n(nk)m k\u3002 MMS SLEPLE STATES STATEK\uff1f \u306e\u3059\u3079\u3066\u306e\u4e3b\u8981\u306a\u8981\u56e0\u304b\u3089 c n= 2 n1\u22c53\u22c55\u22ef(2n\u22121)2\u22c53\u22c54\u22ef(n+1){displaystyle textStyle c_ {n} = 2^{n}\u3001{frac {1cdot 3cdot 5cdots\uff082n-1\uff09} {2cdot 3cdot 4cdots\uff08n+1\uff09}}}}}} \u3001\u5f0f\u3092\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044 \uff08*\uff09\u3001 \u672a\u6e80 2 n {displaystyle 2n} and and  2 n”>\u305f\u3081\u306b  3″>\u9069\u7528\u3055\u308c\u307e\u3059 c 2 = 2 {displaystyle c_ {2} = 2} \u3068 c 3 = 5 {displaystyle c_ {3} = 5} \u30ab\u30bf\u30ed\u30cb\u30a2\u8a9e\u306e\u552f\u4e00\u306e\u6570\u3082\u4e00\u6b21\u6570\u3067\u3059\u3002\u30d5\u30a9\u30fc\u30df\u30e5\u30e9\u3082\u305d\u308c\u3092\u793a\u3057\u3066\u3044\u307e\u3059 c n {displaystyle c_ {n}} \u305d\u306e\u9593\u306e\u5404\u30d7\u30e9\u30a4\u30e0\u756a\u53f7\u3092\u901a\u3057\u3066 n + \u521d\u3081 {displaystyle n+1} \u3068 2 n {displaystyle 2n} \u5206\u88c2\u3057\u3084\u3059\u304f\u3001\u307e\u3063\u305f\u304f\u5947\u5999\u3067\u3059 n + \u521d\u3081 {displaystyle n+1} 2\u306e\u52b9\u529b\u3067\u3059\u3002 \u4e00\u81f4\u306f\u3001\u30a6\u30a9\u30eb\u30c4\u30b9\u30c6\u30f3\u30db\u30eb\u30e0\u306e\u6587\u304b\u3089\u7d9a\u304d\u307e\u3059 \uff08 p n + \u521d\u3081 \uff09\uff09 c pn\u559c\u3093\u3067 \uff08 n + \u521d\u3081 \uff09\uff09 c n\uff08 \u306b\u5bfe\u3057\u3066 p3\uff09\uff09 {displaystyle\uff08p\u3001n+1\uff09\u3001c_ {p\u3001n} equiv\uff08n+1\uff09\u3001c_ {n} {pmod {p^{3}}}}} \u3059\u3079\u3066\u306e\u7d20\u6570\u7528 3″>\u3001\u5408\u540c\u306fWolstenholme\u30d7\u30ea\u30e0\u756a\u53f7\u306b\u9069\u7528\u3055\u308c\u307e\u3059 \u306b\u5bfe\u3057\u3066 \u2061  p 4 {displaystyle operatorname {mod} p^{4}} \u3001\u30d7\u30e9\u30a4\u30e0\u756a\u53f72\u30683\u306b\u9069\u7528\u3055\u308c\u307e\u3059 \u306b\u5bfe\u3057\u3066 \u2061  p 2 {displaystyle operatorname {mod} p^{2}} \u3002 \u7279\u306b\u305d\u3046\u3067\u3059 c pkn \u559c\u3093\u3067 \uff08 n + \u521d\u3081 \uff09\uff09 c n \uff08 \u306b\u5bfe\u3057\u3066 p \uff09\uff09 {displaystyle c_ {p^{k} n} equiv\uff08n+1\uff09\u3001c_ {n} {pmod {p}}} \u3068 c pk\u559c\u3093\u3067 2 \uff08 \u306b\u5bfe\u3057\u3066 p \uff09\uff09 {displaystyle c_ {p^{k}} equiv 2 {pmod {p}}} \u3059\u3079\u3066\u306e\u7d20\u6570\u7528 p {displaystyle p} \u305d\u3057\u3066\u6574\u6570 0″>\u3002 \u30b9\u30bf\u30fc\u30ea\u30f3\u30b0\u30d5\u30a9\u30fc\u30df\u30e5\u30e9\u3092\u633f\u5165\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u30ab\u30bf\u30ed\u30cb\u30a2\u306e\u6570\u306e\u6f38\u8fd1\u7684\u306a\u6319\u52d5\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059 c n\u301c 4n(n+1)\u03c0n\u3002 {displaystyle c_ {n} sim {frac {4^{n}} {\uff08n+1\uff09{sqrt {pi n}}}}\u3002}\u3002 \u76f8\u4e92\u5024\u306e\u5408\u8a08\u306f\u53ce\u675f\u3057\u307e\u3059\uff1a [12\u756a\u76ee] \u2211 n=0\u221e1Cn= 2 + 43\u03c027{displaystyle sum _ {n = 0}^{infty} {frac {1} {c_ {n}}} = 2+ {frac {4 {sqrt {3}} pi} {27}}}}}} \u9069\u7528\u3082\u9069\u7528\u3055\u308c\u307e\u3059\uff08\u7d50\u679c A013709 OEIS 2016\u3067\uff09\uff1a \u2211 n=0\u221e(Cn22n+1)2\uff08 n + \u521d\u3081 \uff09\uff09 = 1\u03c0{displaystyle sum _ {n = 0}^{infty}\u5de6\uff08{frac {c_ {n}} {2^{2n+1}}}\u53f3\uff09^{2}\uff08n+1\uff09= {frac {1} {pi}}}}}}\uff08n+1\uff09= { \u3068\u3057\u3066\u3082  \u2211 n=0\u221e(Cn22n+1)2\uff08 4 n + 3 \uff09\uff09 = \u521d\u3081 {displaystyle sum _ {n = 0}^{infty}\u5de6\uff08{frac {c_ {n}} {2^{2n+1}}}\u53f3\uff09^{2}\uff084n+3\uff09= 1} \u2211 n=0\u221e(Cn22n)2\uff08 n + \u521d\u3081 \uff09\uff09 = 4\u03c0= \u2211 n=\u22121\u221e(Cn22n+1)2{displaystyle sum _ {n = 0}^{infty}\u5de6\uff08{frac {c_ {n}} {2^{2n}}}\u53f3\uff09^{2}\uff08n+1\uff09= {frac {4} {pi}} = sum _ {n = -1}^{{{_ {{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{\uff09{{{{{{{{{{{{{{{{{{ce\uff09\uff09 2^{2n+1}}}\u53f3\uff09^{2}} \uff08Wallis Lambert\u30b7\u30ea\u30fc\u30ba\uff09 c \u22121=  –  12{displaystyle c _ { –  1} =  –  {frac {1} {2}}} \u30d0\u30fc\u30bc\u30eb\u306e\u554f\u984c\u3092\u4f34\u3046Cauchy\u88fd\u54c1\u306e\u5f0f\u306f\u3001\u3053\u308c\u306b\u8d77\u56e0\u3057\u307e\u3059\uff08\u7d50\u679c A281070 OEIS 2017\u3067\uff09\uff1a \u2211 n=0\u221e\u2211 k=0n(Ck22k+1)2k+1(n\u2212k+1)2= \u03c06{displaystyle sum _ {n = 0}^{infty} sum _ {k = 0}^{n}\u5de6\uff08{frac {k_ {k}} {2^{2k+1}}}\u53f3\uff09^{2} {frac {k+1} {{n-k+1\uff09}} {{k+1} 6}}} \u30ab\u30bf\u30ed\u30cb\u30a2\u306e\u6570\u306f\u3001\u30b0\u30e9\u30d5\u7406\u8ad6\u7684\u306b\u30ab\u30a6\u30f3\u30c8\u3055\u308c\u305f\u6728\u3067\u3042\u308b\u591a\u6570\u306e\u30ab\u30a6\u30f3\u30c8\u30bf\u30b9\u30af\u3067\u767a\u751f\u3057\u307e\u3059\u3002\u305d\u3046\u3067\u3059 c n {displaystyle c_ {n}} \u306e\u6570 \u305f\u3068\u3048\u3070\u3001\u3042\u306a\u305f\u306f\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059 n = 3 {displaystyle n = 3} \u306e\u3088\u3046\u306a\u6587\u5b57\u5217 \u30d0\u30c4 \u2217 \u30d0\u30c4 \u2217 \u30d0\u30c4 \u2217 \u30d0\u30c4 {displaystyle x*x*x*x} 5\u3064\u306e\u7570\u306a\u308b\u65b9\u6cd5\u3067\u53ef\u80fd\u306a\u30d6\u30e9\u30b1\u30c3\u30c8\u306b\u8a2d\u5b9a\u3057\u3066\u304f\u3060\u3055\u3044\u3002 ((X\u2217X)\u2217X)\u2217X(X\u2217(X\u2217X))\u2217X(X\u2217X)\u2217(X\u2217X)X\u2217((X\u2217X)\u2217X)X\u2217(X\u2217(X\u2217X)){displaystyle\uff08\uff08x*x\uff09*x\uff09*xqquad\uff08x*\uff08x*x\uff09\uff09*xqquad\uff08x*x\uff09*\uff08x*x\uff09qquad x*\uff08\uff08x*x\uff09*x\uff09qquad x*\uff08x*x\uff09} \u6e1b\u7b97\u306e\u660e\u793a\u7684\u306a\u4f8b\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059 ((10\u22126)\u22123)\u22121(10\u2212(6\u22123))\u22121(10\u22126)\u2212(3\u22121)10\u2212((6\u22123)\u22121)10\u2212(6\u2212(3\u22121)){displayStyle\uff08\uff0810-6\uff09-3\uff09-1QQuad\uff0810-\uff086-3\uff09\uff09-1QQuad\uff0810-6\uff09 – \uff083-1\uff09QQUAD 10-\uff08\uff086-3\uff09-1\uff09QQUAD 10-\uff086-\uff083-1\uff09\uff09} \u305d\u308c\u304c\u7406\u7531\u3067\u3059 c 3= 5 {displaystyle c_ {3} = 5} \u3002\u62ec\u5f27\u5185\u307e\u305f\u306f\u5b8c\u5168\u306a\u8868\u73fe\u306e\u5468\u308a\u306b\u65e2\u306b\u8a2d\u5b9a\u3055\u308c\u305f\u5f0f\u306b\u5197\u9577\u30d6\u30e9\u30b1\u30c3\u30c8\u3092\u8ffd\u52a0\u3059\u308b\u3053\u3068\u306f\u8a31\u53ef\u3055\u308c\u3066\u3044\u307e\u305b\u3093\u3002 0\u30ce\u30c3\u30c8\u306e\u30d0\u30a4\u30ca\u30ea\u30c4\u30ea\u30fc\u304c\u3042\u308a\u3001\u4ed6\u306e\u3059\u3079\u3066\u306e\u30d0\u30a4\u30ca\u30ea\u30c4\u30ea\u30fc\u306f\u3001\u305d\u306e\u5de6\u53f3\u306e\u90e8\u5206\u30c4\u30ea\u30fc\u306e\u7d44\u307f\u5408\u308f\u305b\u306b\u3088\u3063\u3066\u7279\u5fb4\u4ed8\u3051\u3089\u308c\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u30b5\u30d6\u30c4\u30ea\u30fc\u306e\u5834\u5408 \u79c1 {displaystyle i} \u307e\u305f\u3002 j {displaystyle j} \u7d50\u3073\u76ee\u304c\u3042\u308a\u3001\u6728\u5168\u4f53\u306b\u3042\u308a\u307e\u3059 \u79c1 + j + \u521d\u3081 {displaystyle i+j+1} \u30ce\u30fc\u30c9\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u756a\u53f7 c n{displaystyle c_ {n}} \u30d0\u30a4\u30ca\u30ea\u30c4\u30ea\u30fc\u304b\u3089 n {displaystyle n} \u6b21\u306e\u518d\u5e30\u7684\u306a\u8aac\u660e\u3092\u7d50\u3073\u307e\u3059 c 0= \u521d\u3081 {displaystyle c_ {0} = 1} \u3068 Cn= \u2211i=0n\u22121Cide Cn\u22121\u2212i{displaystyle textStyle c_ {n} = sum _ {i = 0}^{n-1} c_ {i} cdot c_ {n-1-i}} \u3059\u3079\u3066\u306e\u6b63\u306e\u6570\u306b\u5bfe\u3057\u3066 n {displaystyle n} \u3002\u305d\u308c\u306b\u7d9a\u304d\u307e\u3059 c n{displaystyle c_ {n}} \u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u4ed8\u304d\u306e\u30ab\u30bf\u30ed\u30cb\u30a2\u756a\u53f7 n {displaystyle n} \u306f\u3002\u3053\u308c\u306f\u3001\u305f\u3068\u3048\u3070\u3001\u975e\u5171\u540c\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u30c1\u30a7\u30fc\u30f3\u4e57\u7b97\u306b\u304a\u3051\u308b\u8a08\u7b97\u30b7\u30fc\u30b1\u30f3\u30b9\u306e\u6570\u306e\u6570\u306e\u5c3a\u5ea6\u3067\u3042\u308a\u3001\u5de7\u307f\u306b\u6700\u9069\u5316\u3055\u308c\u305f\u7559\u3081\u91d1\u306b\u3088\u3063\u3066\u8a08\u7b97\u306e\u53d6\u308a\u7d44\u307f\u3092\u6700\u5c0f\u9650\u306b\u6291\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 \u305d\u306e\u5f8c0\u304b\u3089\u306e\u6b21\u5143\u306e\u30ef\u30f3\u30c0\u30e9\u30fc 2 n {displaystyle 2n} \u958b\u59cb\u3068\u30a8\u30f3\u30c9\u30dd\u30a4\u30f3\u30c8\u304c0\u3067\u3001\u30d1\u30b9\u304c\u6c7a\u3057\u3066 \u30d0\u30c4 {displaystyle x} -achs\u306f\u3042\u308a\u307e\u3059\uff08Dyck\u304b\u3089Walther\u3078\u306e\u3044\u308f\u3086\u308bDyck\u30d1\u30b9\uff09\u3002\u305f\u3068\u3048\u3070\u3001\u3067\u3059 c 3= 5 {displaystyle c_ {3} = 5} \u3001\u3042\u3089\u3086\u308b\u7a2e\u985e\u306e\u30d1\u30b9\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002 \u6b63\u65b9\u5f62\u306e\u30b0\u30ea\u30eb\u306e\u7aef\u306b\u6cbf\u3063\u305f\u5358\u8abf\u306a\u7d4c\u8def n \u00d7 n {displaystyle n} \u5bfe\u89d2\u7dda\u306e\u4e0a\u306e\u70b9\u3092\u542b\u3093\u3067\u3044\u306a\u3044\u4e8c\u6b21\u7d30\u80de\u3002\u5358\u8abf\u306a\u30d1\u30b9\u306f\u5de6\u4e0b\u9685\u304b\u3089\u59cb\u307e\u308a\u3001\u53f3\u4e0a\u9685\u3067\u7aef\u304c\u7d42\u308f\u308a\u3001\u53f3\u307e\u305f\u306f\u4e0a\u306b\u8868\u793a\u3055\u308c\u308b\u7aef\u304b\u3089\u5b8c\u5168\u306b\u69cb\u6210\u3055\u308c\u3066\u3044\u307e\u3059\u3002 14\u306e\u5358\u8abf\u306a\u30d1\u30b9 n = 4 {displaystyle n = 4} \u305d\u308c\u306f\uff1a [13] \u5e45\u306e\u6bb5\u968e\u7684\u306a\u5f62\u3092\u3068\u308b\u6a5f\u4f1a n {displaystyle n} \u3068\u9ad8\u3055 n {displaystyle n} \u3068 n {displaystyle n} \u9577\u65b9\u5f62\u3092\u50be\u3051\u308b\u30bf\u30a4\u30eb\u3002\u306e14\u306e\u30aa\u30d7\u30b7\u30e7\u30f3 n = 4 {displaystyle n = 4} \u305d\u308c\u306f\uff1a [13] \u5019\u88dc\u8005A\u304c\u5019\u88dc\u8005B\u306e\u80cc\u5f8c\u306b\u6c7a\u3057\u3066\u306a\u3044\u3053\u3068\u3092\u30ab\u30a6\u30f3\u30c8\u3059\u308b\u9078\u6319\u3067\u30ab\u30a6\u30f3\u30c8\u3059\u308b\u53ef\u80fd\u6027\u306e\u3042\u308b\u30b3\u30fc\u30b9 n {displaystyle n} \u53d7\u3051\u53d6\u3063\u305f\u58f0\u3068\u6295\u7968\u7528\u7d19\u306f\u3001\u9aa8n\u304b\u3089\u9023\u7d9a\u3057\u3066\u6570\u3048\u3089\u308c\u307e\u3059\u3002\u305f\u3068\u3048\u3070 n = 2 {displaystyle n = 2} \u524d\u63d0\u6761\u4ef6\u3092\u6e80\u305f\u3059\u63cf\u753b\u306e\u53ef\u80fd\u6027\u306e\u3042\u308b\u7d50\u679c\u3067\u3059\u3002 [14] \u65b9\u6cd5\u306e\u53ef\u80fd\u6027 2 n {displaystyle 2n} \u4e38\u3044\u30c6\u30fc\u30d6\u30eb\u306b\u5ea7\u3063\u3066\u3044\u308b\u4eba\u306f\u3001\u8155\u3092\u4ea4\u5dee\u305b\u305a\u306b\u30c6\u30fc\u30d6\u30eb\u306e\u4e0a\u306b\u624b\u3092\u7f6e\u304d\u307e\u3059\u3002 [14] \u30d4\u30fc\u30bf\u30fcJ.\u30d2\u30eb\u30c8\u30f3\u3001\u30b8\u30e3\u30f3\u30da\u30c0\u30fc\u30bb\u30f3\uff1a \u6574\u6570\u30b0\u30ea\u30c3\u30c9\u5185\u306e\u30ab\u30bf\u30ed\u30cb\u30a2\u306e\u6570\u3068\u30d1\u30b9\u3002 \u6570\u5b66\u306e\u8981\u7d2048\u30011993\u3001 doi\uff1a10.5169\/seals-44624\uff0351 \u3001S\u300245ff\u3002 J\u00fcrgenSchmidthammer\uff1a \u30ab\u30bf\u30ed\u30cb\u30a2\u306e\u6570\u3002 \uff08PDF\u30d5\u30a1\u30a4\u30eb; 7.05 MB\uff09\u3001\u5dde\u8a66\u9a13\u306e\u5165\u5834\u4f5c\u696d\u30011996\u5e742\u6708Erlangen\u3002 \u30c8\u30fc\u30de\u30b9\u30fb\u30b3\u30b7\uff1a \u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u3092\u5099\u3048\u305f\u30ab\u30bf\u30ed\u30cb\u30a2\u306e\u6570\u3002 \u30aa\u30c3\u30af\u30b9\u30d5\u30a9\u30fc\u30c9\u5927\u5b66\u51fa\u7248\u5c40\u3001\u30cb\u30e5\u30fc\u30e8\u30fc\u30af2009\u3001ISBN 978-0-19-533454-8\u3002 \u30ea\u30c1\u30e3\u30fc\u30c9\u30fbP\u30fb\u30b9\u30bf\u30f3\u30ea\u30fc\uff1a 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Teubner\u3001Leipzig 1901\uff08\u00a7122\u3001pp\u3002192\u2013194\u304a\u3088\u3073\u00a7124\u3001p\u3002195\u306e\u30ab\u30bf\u30ed\u30cb\u30a2\u3078\u306e\u6570\u5b57\u306e\u5fa9\u5e30\uff09\u3002  \u2191  \u76f8\u4e92\u306e\u30ab\u30bf\u30ed\u30cb\u30a2\u6570\u306e\u5168\u984d\u3002 \u3067\uff1a juanmarqz.wordpress.com\u3002 2009\u5e747\u670829\u65e5\u30012021\u5e741\u670811\u65e5\u30a2\u30af\u30bb\u30b9\u3002  \u2191 a b  Matej Crepinsek\u3001Luka Mernik\uff1a \u30ab\u30bf\u30ed\u30cb\u30a2\u306e\u6570\u95a2\u9023\u306e\u554f\u984c\u3092\u89e3\u6c7a\u3059\u308b\u305f\u3081\u306e\u52b9\u7387\u7684\u306a\u8868\u73fe\u3002 \uff08PDF; 253 kb\uff09\u3002\u306e\uff1a ijpam.eu\u3002 2021\u5e741\u670811\u65e5\u306b\u30a2\u30af\u30bb\u30b9\u3055\u308c\u305f\u7d14\u7c8b\u304a\u3088\u3073\u5fdc\u7528\u6570\u5b66\u306e\u56fd\u969b\u30b8\u30e3\u30fc\u30ca\u30eb\u3002  \u2191 a b  doina logofatu\uff1a C ++\u3092\u4f7f\u7528\u3057\u305f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3068\u554f\u984c\u30bd\u30ea\u30e5\u30fc\u30b7\u30e7\u30f3\u3002 \u7b2c8\u7ae0 \u30ab\u30bf\u30ed\u30cb\u30a2\u306e\u6570\u3002 Vieweg-Verlag\u3001\u7b2c1\u72482006\u3001ISBN 978-3-8348-0126-5\u3001pp\u3002189\u2013206\u3002       (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/16822#breadcrumbitem","name":"\u30ab\u30bf\u30ed\u30cb\u30a2\u30b6\u30fc\u30eb – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2"}}]}]