cp's OEIS Frontend

A361367 Number of weakly 2-connected simple digraphs with n unlabeled nodes.

%I A361367 #15 Mar 10 2023 10:09:19
%S A361367 7,129,7447,1399245,853468061,1774125803324,12983268697759210,
%T A361367 340896057593147232397,32512334188761655225275067,
%U A361367 11365639780174824680535568799361,14668665138188644335253106665956458513,70315069858161131939222463684374769308619684
%N A361367 Number of weakly 2-connected simple digraphs with n unlabeled nodes.
%D A361367 M. Kirchweger, M. Scheucher, and S. Szeider, SAT-Based Generation of Planar Graphs, in preparation.
%o A361367 (PARI) \\ See links in A339645 for combinatorial species functions.
%o A361367 edges(v) = {2*sum(i=2, #v, sum(j=1, i-1, gcd(v[i], v[j]))) + sum(i=1, #v, v[i]-1)}
%o A361367 graphsCycleIndex(n)={my(s=0); forpart(p=n, s+=permcount(p) * 2^edges(p) * sMonomial(p)); s/n!}
%o A361367 graphsSeries(n)={sum(k=0, n, graphsCycleIndex(k)*x^k) + O(x*x^n)}
%o A361367 cycleIndexSeries(n)={my(g=graphsSeries(n), gc=sLog(g), gcr=sPoint(gc)); intformal(x*sSolve( sLog( gcr/(x*sv(1)) ), gcr ), sv(1)) + sSolve(subst(gc, sv(1), 0), gcr)}
%o A361367 { my(N=15); Vec(-2*x^2 + OgfSeries(cycleIndexSeries(N))) } \\ _Andrew Howroyd_, Mar 09 2023
%Y A361367 Directed variant of A002218.
%Y A361367 Cf. A000273, A003085.
%K A361367 nonn
%O A361367 3,1
%A A361367 _Manfred Scheucher_, Mar 09 2023
%E A361367 Terms a(7) and beyond from _Andrew Howroyd_, Mar 09 2023