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

Author

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

Keywords

• nonn

Links

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

Crossrefs

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

Programs

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

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

Extensions

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