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A225213
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.
1
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
OFFSET
1,2
COMMENTS
Row sums = A190314(n)
Sum_{k=1..n} T(n,k)*k = A063169(n)
T(n,n) = (n-1)!
Column 1 = n^n = A000312
Column 2 = A081131
FORMULA
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.
EXAMPLE
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
MATHEMATICA
Table[Table[(j-1)!Binomial[n, j]n^(n-j), {j, 1, n}], {n, 1, 8}]//Grid
CROSSREFS
Sequence in context: A095891 A367304 A095887 * A137906 A139051 A061692
KEYWORD
nonn,tabl
AUTHOR
Geoffrey Critzer, May 01 2013
STATUS
approved