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, 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

Links

Table of n, a(n) for n=1..36.

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

Adjacent sequences: A225210 A225211 A225212 * A225214 A225215 A225216

Keyword

nonn,tabl

Author

Geoffrey Critzer, May 01 2013

Status

approved