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%I M4441 #31 Jul 20 2022 07:25:10
%S 1,7,66,916,16816,373630,9727010,289374391,9677492899,359305262944,
%T 14663732271505,652463078546373,31435363120551013,1630394318463367718,
%U 90570555840053284171,5365261686125108336540,337616338011820295406352,22490263897737210321234701,1581153614004788257326876764
%N Number of semi-regular digraphs (with loops) on n unlabeled nodes with each node having out-degree 2.
%C The directed graphs in this sequence need not be connected, but each node must have out-degree 2. - _Sean A. Irvine_, Apr 09 2015
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Andrew Howroyd, <a href="/A003286/b003286.txt">Table of n, a(n) for n = 2..50</a>
%H S. A. Choudum and K. R. Parthasarathy, <a href="http://dx.doi.org/10.1016/1385-7258(72)90047-9">Semi-regular relations and digraphs</a>, Nederl. Akad. Wetensch. Proc. Ser. A. {75}=Indag. Math. 34 (1972), 326-334.
%H Steve Huntsman, <a href="https://arxiv.org/abs/2003.00944">Generalizing cyclomatic complexity via path homology</a>, arXiv:2003.00944 [cs.SE], 2020.
%H Sean A. Irvine, <a href="/A003286/a003286.png">Illustration of A003286(3)</a>.
%t permcount[v_] := Module[{m = 1, s = 0, k = 0, t}, For[i = 1, i <= Length[v], i++, t = v[[i]]; k = If[i > 1 && t == v[[i - 1]], k + 1, 1]; m *= t*k; s += t]; s!/m];
%t edges[v_, k_] := Product[SeriesCoefficient[Product[g = GCD[v[[i]], v[[j]]]; (1 + x^(v[[j]]/g) + O[x]^(k + 1))^g, {j, 1, Length[v]}], {x, 0, k}], {i, 1, Length[v]}];
%t a[n_] := Module[{s = 0}, Do[s += permcount[p]*edges[p, 2], {p, IntegerPartitions[n]}]; s/n!];
%t Table[a[n], {n, 2, 20}] (* _Jean-François Alcover_, Jul 20 2022, after _Andrew Howroyd_ in A259471 *)
%Y Column k=2 of A259471.
%Y Cf. A129524.
%K nonn,nice
%O 2,2
%A _N. J. A. Sloane_
%E a(7)-a(9) from _Sean A. Irvine_, Apr 11 2015
%E Terms a(10) and beyond from _Andrew Howroyd_, Sep 13 2020
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