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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.

%I A225213 #6 May 02 2013 06:24:17
%S A225213 1,4,1,27,9,2,256,96,32,6,3125,1250,500,150,24,46656,19440,8640,3240,
%T A225213 864,120,823543,352947,168070,72030,24696,5880,720,16777216,7340032,
%U A225213 3670016,1720320,688128,215040,46080,5040
%N 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.
%C A225213 Row sums = A190314(n)
%C A225213   Sum_{k=1..n} T(n,k)*k = A063169(n)
%C A225213   T(n,n) = (n-1)!
%C A225213   Column 1 = n^n = A000312
%C A225213   Column 2 = A081131
%F A225213 T(n,k) = (k-1)!*binomial(n,k)*n^(n-k)
%F A225213 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.
%e A225213 1,
%e A225213 4,      1,
%e A225213 27,     9,      2,
%e A225213 256,    96,     32,     6,
%e A225213 3125,   1250,   500,    150,   24,
%e A225213 46656,  19440,  8640,   3240,  864,   120,
%e A225213 823543, 352947, 168070, 72030, 24696, 5880, 720
%t A225213 Table[Table[(j-1)!Binomial[n,j]n^(n-j),{j,1,n}],{n,1,8}]//Grid
%K A225213 nonn,tabl
%O A225213 1,2
%A A225213 _Geoffrey Critzer_, May 01 2013