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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.

%I A355612 #6 Jul 10 2022 08:28:07
%S A355612 1,1,4,52,2524,629296,750098464,3540134362192,63605185617860464,
%T A355612 4402130837352016607296,1190565802204629673473661504,
%U A355612 1270503156085666608161173288964992,5381113705726490960372769906727545572224,90765998703828737395601069325546106634460887296,6109068274998388232409260496587163340177606642565219584
%N 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.
%C A355612 Here a digraph can have both a directed edge from x to y and y to x but no self loops are allowed.
%F A355612 E.g.f.:  D(S(x)-1) where D(x),S(x) are the e.g.f.'s for A003024 and A003030 respectively.
%t A355612 nn = 14; d[x_] := Total[Cases[Import["https://oeis.org/A003024/b003024.txt",
%t A355612       "Table"], {_, _}][[All, 2]]*Table[x^(i - 1)/(i - 1)!, {i, 1, 41}]];
%t A355612 s[x_] := Total[ Prepend[Cases[Import["https://oeis.org/A003030/b003030.txt",
%t A355612        "Table"], {_, _}][[All, 2]], 1]* Table[x^(i - 1)/(i - 1)!, {i, 1, 59}]];
%t A355612 Range[0, nn]! CoefficientList[Series[d[s[x] - 1], {x, 0, nn}], x]
%Y A355612 Cf. A003024, A003030.
%K A355612 nonn
%O A355612 0,3
%A A355612 _Geoffrey Critzer_, Jul 09 2022