A102597 Number of n-node labeled connected oriented graphs whose underlying graphs are mating graphs, cf. A006024.

1, 1, 2, 8, 352, 32768, 9072896, 7389698048, 17695056717824, 124756911516516352, 2594584522679818518528, 159570269132472101976145920, 29103249711329178773313159168000, 15783921191009840333055992641622114304, 25514864105378775907711095288995558725779456

Offset

0,3

Links

Andrew Howroyd, Table of n, a(n) for n = 0..50

Formula

E.g.f.: 1 + x + log(B(x)/(1 + x)) where B(x) is the e.g.f. of A102596. - Andrew Howroyd, Jan 20 2024

Prog

(PARI) \\ b(n) is A102596(n); permcount, edges defined in A369283.
b(n) = {my(s=0); forpart(p=n, s += permcount(p)*(-1)^(n-#p)*edges(p, w->1 + 2^w)); s}
seq(n) = {Vec(serlaplace(1 + x + log(sum(k=0, n, b(k)*x^k/k!, O(x*x^n))/(1 + x))))} \\ Andrew Howroyd, Jan 20 2024

Crossrefs

Cf. A006024, A102580 (digraphs), A102596 (not necessarily connected), A102599 (unlabeled), A369283.

Sequence in context: A013176 A220904 A009489 * A009836 A012342 A012348

Adjacent sequences: A102594 A102595 A102596 * A102598 A102599 A102600

Keyword

nonn

Author

Goran Kilibarda, Zoran Maksimovic, Vladeta Jovovic, Jan 22 2005

Extensions

a(0)=1 prepended and a(13) onwards from Andrew Howroyd, Jan 20 2024

Status

approved