OFFSET
0,4
COMMENTS
Row sums = n^(n+1) = Sum_{k=1..n} T(n,k)*k.
Column for k=0 is A209290.
Distribution is Poisson with mean = 1.
LINKS
Alois P. Heinz, Rows n = 0..140, flattened
FORMULA
T(n,k) = binomial(n,k)*(n-1)^(n-k)*n.
EXAMPLE
0;
0, 1;
2, 4, 2;
24, 36, 18, 3;
324, 432, 216, 48, 4;
5120, 6400, 3200, 800, 100, 5;
93750, 112500, 56250, 15000, 2250, 180, 6;
1959552, 2286144, 1143072, 317520, 52920, 5292, 294, 7;
MATHEMATICA
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
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Geoffrey Critzer, Jan 21 2013
STATUS
approved