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A361367
Number of weakly 2-connected simple digraphs with n unlabeled nodes.
1
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.
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.
Sequence in context: A187237 A095885 A361369 * A332050 A134056 A123036
KEYWORD
nonn
AUTHOR
Manfred Scheucher, Mar 09 2023
EXTENSIONS
Terms a(7) and beyond from Andrew Howroyd, Mar 09 2023
STATUS
approved