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%I #16 Jan 22 2013 19:28:32
%S 0,0,1,2,4,2,24,36,18,3,324,432,216,48,4,5120,6400,3200,800,100,5,
%T 93750,112500,56250,15000,2250,180,6,1959552,2286144,1143072,317520,
%U 52920,5292,294,7,46118408,52706752,26353376,7529536,1344560,153664,10976,448,8
%N Triangular array read by rows: T(n,k) is the number of elements x in {1,2,...,n} such that |(f^-1)(x)| = k over all functions f:{1,2,...,n}->{1,2,...,n}; n>=0, 0<=k<=n.
%C Row sums = n^(n+1) = Sum_{k=1..n} T(n,k)*k.
%C Column for k=0 is A209290.
%C Distribution is Poisson with mean = 1.
%H Alois P. Heinz, <a href="/A210457/b210457.txt">Rows n = 0..140, flattened</a>
%F T(n,k) = binomial(n,k)*(n-1)^(n-k)*n.
%e 0;
%e 0, 1;
%e 2, 4, 2;
%e 24, 36, 18, 3;
%e 324, 432, 216, 48, 4;
%e 5120, 6400, 3200, 800, 100, 5;
%e 93750, 112500, 56250, 15000, 2250, 180, 6;
%e 1959552, 2286144, 1143072, 317520, 52920, 5292, 294, 7;
%t nn=7;f[list_]:=Sum[list[[i]]*(i-1),{i,1,Length[list]}];g[list_]:= Select[list,#>0&];Prepend[Insert[Map[g,Transpose[Table[Table[f[ CoefficientList[n!Coefficient[Series[(Exp[x]-x^m/m!+y x^m/m!)^n,{x,0,nn}],x^n],y]],{n,1,nn}],{m,0,nn}]]],0,{1,1}],{0}]//Grid
%K nonn,tabl
%O 0,4
%A _Geoffrey Critzer_, Jan 21 2013
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