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Search: id:A090657
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| A090657 |
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Triangle read by rows: T(n,k) = number of functions from [1,2,...,n] to [1,2,...,n] such that the image contains k elements (k in [1,2,...,n]). |
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7
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| 1, 0, 1, 0, 2, 2, 0, 3, 18, 6, 0, 4, 84, 144, 24, 0, 5, 300, 1500, 1200, 120, 0, 6, 930, 10800, 23400, 10800, 720, 0, 7, 2646, 63210, 294000, 352800, 105840, 5040, 0, 8, 7112, 324576, 2857680, 7056000, 5362560, 1128960, 40320
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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{1}, {0, 1}, {0, 2, 2}, {0, 3, 18, 6}, {0, 4, 84, 144, 24}, ...
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FORMULA
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T(n, k) = C(n, k)*A048993(n, k)*k! where A048993 = numbers of Stirling2. T(n, k) = A008279(n, k) *A048993(n, k). T(n, k) = A019538(n, k)* C(n, k) . Sum(k>=0, T(n, k)) = n^n; see A000312.
a(n,k) = k*a(n-1,k)*C(n,k)/C(n-1,k) + (n-(k-1))*a(n-1,k-1)*C(n,k-1)/C(n-1,k-1), with a(n,1) = n and a(n,n) = n! - Joshua Zucker (joshua.zucker(AT)stanfordalumni.org), Nov 27 2006
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CROSSREFS
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Cf. A007318 A048993 A019538 A08279 A000312.
Sequence in context: A118262 A011137 A143396 this_sequence A108563 A138476 A131381
Adjacent sequences: A090654 A090655 A090656 this_sequence A090658 A090659 A090660
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Dec 14 2003
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EXTENSIONS
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Revised description from Jan Maciak, Apr 25 2004
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