A355612 Number of labeled digraphs on [n] such that for any pair C_1,C_2 of distinct strongly connected components, if x in C_1 is directed to y in C_2 then every vertex in C_1 is directed to every vertex in C_2.

1, 1, 4, 52, 2524, 629296, 750098464, 3540134362192, 63605185617860464, 4402130837352016607296, 1190565802204629673473661504, 1270503156085666608161173288964992, 5381113705726490960372769906727545572224, 90765998703828737395601069325546106634460887296, 6109068274998388232409260496587163340177606642565219584

Offset: 0

Author

Geoffrey Critzer, Jul 09 2022

Keywords

• nonn

Comments

Here a digraph can have both a directed edge from x to y and y to x but no self loops are allowed.

Crossrefs

Cf. A003024, A003030.

Programs

Mathematica

nn = 14; d[x_] := Total[Cases[Import["https://oeis.org/A003024/b003024.txt",
      "Table"], {, }][[All, 2]]*Table[x^(i - 1)/(i - 1)!, {i, 1, 41}]];
s[x_] := Total[ Prepend[Cases[Import["https://oeis.org/A003030/b003030.txt",
       "Table"], {, }][[All, 2]], 1]* Table[x^(i - 1)/(i - 1)!, {i, 1, 59}]];
Range[0, nn]! CoefficientList[Series[d[s[x] - 1], {x, 0, nn}], x]

Formula

E.g.f.: D(S(x)-1) where D(x),S(x) are the e.g.f.'s for A003024 and A003030 respectively.