OFFSET
0,4
COMMENTS
Here, a strongly connected component is isolated if it is both an in-component and an out-component. A component is an in-component (out-component) if it corresponds to a node with outdegree (indegree) zero in the condensation of the digraph.
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.
FORMULA
EXAMPLE
1;
0, 1;
2, 1, 1;
36, 24, 3, 1;
2240, 1762, 87, 6, 1;
462720, 577000, 8630, 215, 10, 1;
...
MATHEMATICA
nn = 8; 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}]];
d[z_] := Sum[2^(n (n - 1)) z^n/n!, {n, 0, nn}]; Table[Take[(Table[n!, {n, 0, nn}] CoefficientList[ Series[Exp[(u - 1) s[z]] d[z], {z, 0, nn}], {z, u}])[[i]],
i], {i, 1, nn + 1}] // Grid
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Geoffrey Critzer, Apr 11 2023
STATUS
approved