OFFSET
0,8
LINKS
R. P. Stanley, Acyclic orientation of graphs, Discrete Math. 5 (1973), 171-178.
FORMULA
Let E(x) = Sum_{n>=0} x^n/(n!*2^binomial(n,2)). Then Sum_{n>=0} T(n,k)*x^n/(n!*2^binomial(n,2)) = 1/E(-x)^k.
T(n,k) = (-1)^n p_n(-k) where p_n is the n-th polynomial described in A219765.
EXAMPLE
Array begins
1, 1, 1, 1, 1, 1, ...
0, 1, 2, 3, 4, 5, ...
0, 3, 10, 21, 36, 55, ...
0, 25, 122, 339, 724, 1325, ...
0, 543, 3550, 12477, 32316, 69595, ...
0, 29281, 241442, 1035843, 3180484, 7934885, ...
...
MATHEMATICA
nn = 6; e[x_] := Sum[x^n/(n! 2^Binomial[n, 2]), {n, 0, nn}];
Prepend[Table[Table[n! 2^Binomial[n, 2], {n, 0, nn}] CoefficientList[
Series[1/e[-x]^k, {x, 0, nn}], x], {k, 1, nn}], PadRight[{1}, nn + 1]] // Transpose // Grid
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Geoffrey Critzer, Jan 21 2021
STATUS
approved