OFFSET
0,3
COMMENTS
Here, an in-node is a node whose outdegree is zero. An out-node is a node whose in-degree is zero. The in-node is not necessarily distinct from the out-node.
LINKS
E. de Panafieu and S. Dovgal, Symbolic method and directed graph enumeration, arXiv:1903.09454 [math.CO], 2019.
R. W. Robinson, Counting digraphs with restrictions on the strong components, Combinatorics and Graph Theory '95 (T.-H. Ku, ed.), World Scientific, Singapore (1995), 343-354.
MATHEMATICA
nn = 14; B[n_] := n! 2^Binomial[n, 2] ; e[z_] := Sum[z^n/B[n], {n, 0, nn}];
g[z_] := Sum[2^(n (n - 1)) z^n/B[n], {n, 0, nn}]; egf[ggf_] := Normal[Series[ggf, {z, 0, nn}]] /. Table[z^i -> z^i*2^Binomial[i, 2], {i, 0, nn}]; Table[n!, {n, 0, nn}] Map[Coefficient[#, u v] &, CoefficientList[Series[Exp[(u - 1) ( v - 1) z] egf[e[(u - 1) z] g[z] e[(v - 1) z]], {z, 0, nn}], z]]
CROSSREFS
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Apr 09 2023
STATUS
approved