cp's OEIS Frontend

A366350 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 then there is a directed edge from x to y or from y to x.

%I A366350 #16 Oct 08 2023 08:53:35
%S A366350 1,2,12,240,29056,18656960,47473519744,452285200546816,
%T A366350 16275391021965395968,2253596336074652670148608,
%U A366350 1219094258112479334941371285504,2601963635581642923807860961645363200
%N A366350 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 then there is a directed edge from x to y or from y to x.
%C A366350 Equivalently, a(n) is the number of n x n binary relation matrices such that each of the blocks above the diagonal of its Frobenius normal form is a 1-block (a block containing all 1's).  See Gregory, Kirkland and Pullman for definition of Frobenius normal form.
%H A366350 D. A. Gregory, S. Kirkland, and N. J. Pullman, <a href="https://doi.org/10.1016/0024-3795(93)90323-G">Power convergent Boolean matrices</a>, Linear Algebra and its Applications, Volume 179, 15 January 1993, Pages 105-117.
%F A366350 E.g.f.: 1/(1-(s(2x)-1)) where s(x) is the e.g.f. for A003030.
%t A366350 nn = 11; strong =Select[Import["https://oeis.org/A003030/b003030.txt", "Table"],
%t A366350    Length@# == 2 &][[All, 2]]; s[x_] := Total[Prepend[strong Table[x^i/i!, {i, 1, 58}], 1]];Table[n!, {n, 0, nn}] CoefficientList[Series[1/(1 - (s[x + x] - 1)), {x, 0, nn}], x]
%Y A366350 Cf. A003030.
%K A366350 nonn
%O A366350 0,2
%A A366350 _Geoffrey Critzer_, Oct 07 2023