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A225213
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Triangular array read by rows. T(n,k) is the number of cycles in the digraph representation of all functions f:{1,2,...,n}->{1,2,...,n} that have length k; 1<=k<=n.
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1
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1, 4, 1, 27, 9, 2, 256, 96, 32, 6, 3125, 1250, 500, 150, 24, 46656, 19440, 8640, 3240, 864, 120, 823543, 352947, 168070, 72030, 24696, 5880, 720, 16777216, 7340032, 3670016, 1720320, 688128, 215040, 46080, 5040
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OFFSET
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1,2
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COMMENTS
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T(n,n) = (n-1)!
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LINKS
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FORMULA
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T(n,k) = (k-1)!*binomial(n,k)*n^(n-k)
E.g.f. for column k: A(x)^k/k * B(x) where A(x) is e.g.f. for A000169 and B(x) is e.g.f. for A000312.
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EXAMPLE
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1,
4, 1,
27, 9, 2,
256, 96, 32, 6,
3125, 1250, 500, 150, 24,
46656, 19440, 8640, 3240, 864, 120,
823543, 352947, 168070, 72030, 24696, 5880, 720
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MATHEMATICA
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Table[Table[(j-1)!Binomial[n, j]n^(n-j), {j, 1, n}], {n, 1, 8}]//Grid
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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