[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/3354#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/3354","headline":"Euler\u306e\u6570\u5b57-Wikipedia\u3001\u7121\u6599\u767e\u79d1\u4e8b\u5178","name":"Euler\u306e\u6570\u5b57-Wikipedia\u3001\u7121\u6599\u767e\u79d1\u4e8b\u5178","description":"before-content-x4 2016 &#8211; 12\u5e74\u306e\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u63d0\u4f9b\u3055\u308c\u305f\u60c5\u5831\u306e\u691c\u8a3c\u304c\u5fc5\u8981\u3067\u3059\u3002 \u4fe1\u983c\u3067\u304d\u308b\u60c5\u5831\u6e90\u306f\u3001\u597d\u307e\u3057\u304f\u306f\u66f8\u8a8c\u7684\u306a\u811a\u6ce8\u306e\u5f62\u3067\u4e0e\u3048\u3089\u308c\u308b\u3079\u304d\u3067\u3059\u3002 \u8a18\u4e8b\u306e\u4e00\u90e8\u307e\u305f\u306f\u3059\u3079\u3066\u306e\u60c5\u5831\u3067\u3055\u3048\u3001\u771f\u5b9f\u3067\u306f\u306a\u3044\u5834\u5408\u304c\u3042\u308a\u307e\u3059\u3002\u30bd\u30fc\u30b9\u3092\u6b20\u3044\u3066\u3044\u308b\u3088\u3046\u306b\u3001\u305d\u308c\u3089\u306f\u6311\u6226\u3057\u3066\u524a\u9664\u3055\u308c\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002 \u6b20\u9665\u3092\u6392\u9664\u3057\u305f\u5f8c\u3001\u3053\u306e\u8a18\u4e8b\u304b\u3089\u30c6\u30f3\u30d7\u30ec\u30fc\u30c8{{refine}}\u3092\u524a\u9664\u3057\u307e\u3059\u3002 \u30aa\u30a4\u30e9\u30fc\u306e\u6570 &#8211; \u30ec\u30ca\u30fc\u30c9\u30aa\u30a4\u30e9\u30fc\u304c\u7814\u7a76\u3057\u305f2\u3064\u306e\u6570\u5024\u30eb\u30fc\u30c8\u3002 after-content-x4 \u9806\u5217\u306e\u6570\u3092\u8aac\u660e\u3057\u3066\u304f\u3060\u3055\u3044 n {displaystyle n} &#8211; \u6240\u6709\u306e\u8981\u7d20\u30b3\u30ec\u30af\u30b7\u30e7\u30f3 after-content-x4 k {displaystyle","datePublished":"2019-10-22","dateModified":"2019-10-22","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/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\/6\/64\/Question_book-4.svg\/50px-Question_book-4.svg.png","url":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/6\/64\/Question_book-4.svg\/50px-Question_book-4.svg.png","height":"39","width":"50"},"url":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/3354","wordCount":4242,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x42016  &#8211;  12\u5e74\u306e\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u63d0\u4f9b\u3055\u308c\u305f\u60c5\u5831\u306e\u691c\u8a3c\u304c\u5fc5\u8981\u3067\u3059\u3002 \u4fe1\u983c\u3067\u304d\u308b\u60c5\u5831\u6e90\u306f\u3001\u597d\u307e\u3057\u304f\u306f\u66f8\u8a8c\u7684\u306a\u811a\u6ce8\u306e\u5f62\u3067\u4e0e\u3048\u3089\u308c\u308b\u3079\u304d\u3067\u3059\u3002 \u8a18\u4e8b\u306e\u4e00\u90e8\u307e\u305f\u306f\u3059\u3079\u3066\u306e\u60c5\u5831\u3067\u3055\u3048\u3001\u771f\u5b9f\u3067\u306f\u306a\u3044\u5834\u5408\u304c\u3042\u308a\u307e\u3059\u3002\u30bd\u30fc\u30b9\u3092\u6b20\u3044\u3066\u3044\u308b\u3088\u3046\u306b\u3001\u305d\u308c\u3089\u306f\u6311\u6226\u3057\u3066\u524a\u9664\u3055\u308c\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002 \u6b20\u9665\u3092\u6392\u9664\u3057\u305f\u5f8c\u3001\u3053\u306e\u8a18\u4e8b\u304b\u3089\u30c6\u30f3\u30d7\u30ec\u30fc\u30c8{{refine}}\u3092\u524a\u9664\u3057\u307e\u3059\u3002 \u30aa\u30a4\u30e9\u30fc\u306e\u6570  &#8211; \u30ec\u30ca\u30fc\u30c9\u30aa\u30a4\u30e9\u30fc\u304c\u7814\u7a76\u3057\u305f2\u3064\u306e\u6570\u5024\u30eb\u30fc\u30c8\u3002        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u9806\u5217\u306e\u6570\u3092\u8aac\u660e\u3057\u3066\u304f\u3060\u3055\u3044 n {displaystyle n}  &#8211; \u6240\u6709\u306e\u8981\u7d20\u30b3\u30ec\u30af\u30b7\u30e7\u30f3        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4k {displaystyle k}  \u4e18 \u3001\u3064\u307e\u308a k {displaystyle k} \u305d\u306e\u30a2\u30a4\u30c6\u30e0 pi j< pi j+1\u3002 {displaystyle pi _ {j} 1k\u27e9+ \uff08 n  &#8211;  k \uff09\uff09 \u27e8n\u22121k\u22121\u27e9{displayStyle leftlangle {begin {matrix} n \\ kend {matrix}} rightrangle =\uff08k +1\uff09leftlangle {begin {matrix} n-1 \\ kend {matrix}} rightrangle +\uff08n-k\uff09leftlangle {begin {matrix} n-1 \\ k-dend {} righ \u5883\u754c\u6761\u4ef6\u4ed8\u304d \u27e800\u27e9= \u521d\u3081 \u3001 \u27e8n0\u27e9= \u521d\u3081 \u3001 \u27e8nn\u27e9= 0\u3002 {displaystyle leftlangle {begin {matrix} 0 \\ 0end {matrix}} rightrangle = 1\u3001quad leftlangle {begin {matrix} n \\ 0end {matrix}} rightrangle = 1\u3001quad leftlangle {begin {matrix} \u6570\u5024\u4e09\u89d2\u5f62 [ \u7de8\u96c6 | \u30b3\u30fc\u30c9\u3092\u7de8\u96c6\u3057\u307e\u3059 ] n\/k\u00a00\u00a0\u00a01\u00a0234567\u00a0\u00a08\u00a0\u00a0\u00a09011102110314104111111051266626106157302302571071120119124161191120108124742931561915619429324710915021460888234156190882341460850210{displaystyle {begin{matrix}mathbf {n} \/{mathit {k}}&#038; {mathit {0}} &#038; {mathit {1}} &#038;{mathit {2}}&#038;{mathit {3}}&#038;{mathit {4}}&#038;{mathit {5}}&#038;{mathit {6}}&#038;{mathit {7}}&#038;  {mathit {8}}  &#038; {mathit {9}}\\mathbf {0} &#038;1\\mathbf {1} &#038;1&#038;0\\mathbf {2} &#038;1&#038;1&#038;0\\mathbf {3} &#038;1&#038;4&#038;1&#038;0\\mathbf {4} &#038;1&#038;11&#038;11&#038;1&#038;0\\mathbf {5} &#038;1&#038;26&#038;66&#038;26&#038;1&#038;0\\mathbf {6} &#038;1&#038;57&#038;302&#038;302&#038;57&#038;1&#038;0\\mathbf {7} &#038;1&#038;120&#038;1191&#038;2416&#038;1191&#038;120&#038;1&#038;0\\mathbf {8} &#038;1&#038;247&#038;4293&#038;15619&#038;15619&#038;4293&#038;247&#038;1&#038;0\\mathbf {9} &#038;1&#038;502&#038;14608&#038;88234&#038;156190&#038;88234&#038;14608&#038;502&#038;1&#038;0end{matrix}}} \u30d7\u30ed\u30d1\u30c6\u30a3 [ \u7de8\u96c6 | \u30b3\u30fc\u30c9\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u27e8nk\u27e9= \u2211m=0k(n+1m)\uff08 k + \u521d\u3081  &#8211;  m )n\uff08  &#8211;  \u521d\u3081 )m{displayStyle leftlangle {begin {matrix} n \\ kend {matrix}} rightrangle = sum _ {m = 0}^{k} {n+1 choose m}\uff08k+1-m\uff09^{n}\uff08-1\uff09^{m}}}}}} \u27e8nk\u27e9= \u2211m=0k(n+1m)\uff08 k + \u521d\u3081  &#8211;  m )n\uff08  &#8211;  4 )M{displaystyle\u5de6langle{begin {matrix} n \\ kend {matrix}} rightrangle = sum _ {m = 0}^{n+1 choose m}\uff08k+1-m\uff09^{n}\uff08-4\uff09^{m}}}}}} \u3053\u308c\u3089\u306e\u6570\u5b57\u306f\u6b21\u306e\u3088\u3046\u306b\u30de\u30fc\u30af\u3055\u308c\u3066\u3044\u307e\u3059\u3002 \u27e8\u27e8nk\u27e9\u27e9{displaystyle leftlangle !! leftlangle {begin {matrix} n \\ kend {matrix}} rightrangle !! rightrangle} \u30ad\u30e3\u30e9\u30af\u30bf\u30fc\u306e\u518d\u5e30\u65b9\u7a0b\u5f0f\u3092\u6e80\u305f\u3057\u307e\u3059\u3002 \u27e8\u27e8nk\u27e9\u27e9= \uff08 k + \u521d\u3081 \uff09\uff09 \u27e8\u27e8n\u22121k\u27e9\u27e9+ \uff08 2 n  &#8211;  \u521d\u3081  &#8211;  k \uff09\uff09 \u27e8\u27e8n\u22121k\u22121\u27e9\u27e9{displaystyle leftlangle !!\u5de6rangle {begin {matrix} n \\ kend {matrix}} rightrangle !! rightrangle =\uff08k +1\uff09leftlangle !! leftlangle {begin {matrix} n-1 \\ kend {matrix}} rightrangle !! rightrangle !! -1END {matrix}} rightrangle !! rightrangle} \u5883\u754c\u6761\u4ef6\u4ed8\u304d \u27e8\u27e800\u27e9\u27e9= \u521d\u3081 \u3001 \u27e8\u27e8n0\u27e9\u27e9= \u521d\u3081 \u3001 \u27e8\u27e8nn\u27e9\u27e9= 0\u3002 {displaystyle leftlangle !! leftlangle {begin {matrix} 0 \\ 0end {matrix}} rightrangle !! rightrangle = 1\u3001quad leftlangle !! leftlangle {begin {matrix} n \\ 0end {matrix}} rightrangle !! rightrangle !! }} rightrangle !! rightrangle = 0\u3002} \u6570\u5024\u4e09\u89d2\u5f62 [ \u7de8\u96c6 | \u30b3\u30fc\u30c9\u3092\u7de8\u96c6\u3057\u307e\u3059 ] n\/k\u00a00\u00a0\u00a01\u00a0234567\u00a0\u00a08\u00a0\u00a0\u00a0901110212031860412258240515232844412006111414524400370872007124056103212058140339845040081494199501958006440207853043411364032009110046726010625005765500124400641102629637339203628800{displaystyle {begin{matrix}mathbf {n} \/{mathit {k}}&#038; {mathit {0}} &#038; {mathit {1}} &#038;{mathit {2}}&#038;{mathit {3}}&#038;{mathit {4}}&#038;{mathit {5}}&#038;{mathit {6}}&#038;{mathit {7}}&#038;  {mathit {8}}  &#038; {mathit {9}}\\mathbf {0} &#038;1\\mathbf {1} &#038;1&#038;0\\mathbf {2} &#038;1&#038;2&#038;0\\mathbf {3} &#038;1&#038;8&#038;6&#038;0\\mathbf {4} &#038;1&#038;22&#038;58&#038;24&#038;0\\mathbf {5} &#038;1&#038;52&#038;328&#038;444&#038;120&#038;0\\mathbf {6} &#038;1&#038;114&#038;1452&#038;4400&#038;3708&#038;720&#038;0\\mathbf {7} &#038;1&#038;240&#038;5610&#038;32120&#038;58140&#038;33984&#038;5040&#038;0\\mathbf {8} &#038;1&#038;494&#038;19950&#038;195800&#038;644020&#038;785304&#038;341136&#038;40320&#038;0\\mathbf {9} &#038;1&#038;1004&#038;67260&#038;1062500&#038;5765500&#038;12440064&#038;11026296&#038;3733920&#038;362880&#038;0end{matrix}}}       (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\/wiki47\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/3354#breadcrumbitem","name":"Euler\u306e\u6570\u5b57-Wikipedia\u3001\u7121\u6599\u767e\u79d1\u4e8b\u5178"}}]}]