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

7, 129, 7447, 1399245, 853468061, 1774125803324, 12983268697759210, 340896057593147232397, 32512334188761655225275067, 11365639780174824680535568799361, 14668665138188644335253106665956458513, 70315069858161131939222463684374769308619684

Offset

3,1

References

M. Kirchweger, M. Scheucher, and S. Szeider, SAT-Based Generation of Planar Graphs, in preparation.

Links

Table of n, a(n) for n=3..14.

Prog

(PARI) \\ See links in A339645 for combinatorial species functions.
edges(v) = {2*sum(i=2, #v, sum(j=1, i-1, gcd(v[i], v[j]))) + sum(i=1, #v, v[i]-1)}
graphsCycleIndex(n)={my(s=0); forpart(p=n, s+=permcount(p) * 2^edges(p) * sMonomial(p)); s/n!}
graphsSeries(n)={sum(k=0, n, graphsCycleIndex(k)*x^k) + O(x*x^n)}
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)}
{ my(N=15); Vec(-2*x^2 + OgfSeries(cycleIndexSeries(N))) } \\ Andrew Howroyd, Mar 09 2023

Crossrefs

Directed variant of A002218.

Cf. A000273, A003085.

Sequence in context: A187237 A095885 A361369 * A332050 A134056 A123036

Adjacent sequences: A361364 A361365 A361366 * A361368 A361369 A361370

Keyword

nonn

Author

Manfred Scheucher, Mar 09 2023

Extensions

Terms a(7) and beyond from Andrew Howroyd, Mar 09 2023

Status

approved