A366396 - OEIS

A366396

Number of labeled directed graphs on [n] with self loops allowed such that the following implication holds for all x,y in [n]. If x and y are in distinct strongly connected components and y is reachable from x then there is a directed edge from x to y.

%I #9 Oct 09 2023 12:57:28

%S 1,2,16,368,34624,19194752,47730489856,452968293106688,

%T 16282682505688059904,2253889950034687424110592,

%U 1219139359408849690950674415616,2601990460616856808147727573494857728,22041041736721298233193355574294486210576384

%N Number of labeled directed graphs on [n] with self loops allowed such that the following implication holds for all x,y in [n]. If x and y are in distinct strongly connected components and y is reachable from x then there is a directed edge from x to y.

%F E.g.f.: p(s(2x)-1) where p(x) is the e.g.f. for A001025 and s(x) is the e.g.f. for A003030.

%t nn = 12; posets = Select[Import["https://oeis.org/A001035/b001035.txt", "Table"],

%t Length@# == 2 &][[All, 2]];p[x_] := Total[posets Table[x^i/i!, {i, 0, 18}]]; strong = Select[Import["https://oeis.org/A003030/b003030.txt", "Table"],

%t Length@# == 2 &][[All, 2]]; s[x_] := Total[Prepend[strong Table[x^i/i!, {i, 1, 58}], 1]];Table[n!, {n, 0, nn}] CoefficientList[Series[p[s[2 x] - 1], {x, 0, nn}], x]

%Y Cf. A366350, A001035, A003030.

%K nonn

%O 0,2

%A _Geoffrey Critzer_, Oct 08 2023