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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 (list; table; graph; refs; listen; history; text; internal format)
 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 LINKS 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: A118283 A095891 A095887 * A137906 A139051 A061692 Adjacent sequences:  A225210 A225211 A225212 * A225214 A225215 A225216 KEYWORD nonn,tabl AUTHOR Geoffrey Critzer, May 01 2013 STATUS approved

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Last modified September 23 11:24 EDT 2021. Contains 347612 sequences. (Running on oeis4.)