OFFSET
0,5
LINKS
E. de Panafieu and S. Dovgal, Symbolic method and directed graph enumeration, arXiv:1903.09454 [math.CO], 2019.
EXAMPLE
Triangle T(n,k) begins:
1;
0, 1;
1, 2, 1;
27, 27, 9, 1;
2401, 1372, 294, 28, 1;
759375, 253125, 33750, 2250, 75, 1;
...
MATHEMATICA
nn = 6; B[n_] := n! 2^Binomial[n, 2] ; strong =Select[Import["https://oeis.org/A003030/b003030.txt", "Table"], Length@# == 2 &][[All, 2]]; s[z_] := Total[strong Table[z^i/i!, {i, 1, 58}]];
ggf[egf_] := Normal[Series[egf, {z, 0, nn}]] /.Table[z^i -> z^i/2^Binomial[i, 2], {i, 0, nn}]; Table[ Take[(Table[B[n], {n, 0, nn}] CoefficientList[ Series[ggf[Exp[(u - 1) z]]/ggf[Exp[-s[z]]], {z, 0, nn}], {z, u}])[[i]], i], {i, 1, nn + 1}]
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Geoffrey Critzer, Apr 03 2023
STATUS
approved