login
A102597
Number of n-node labeled connected oriented graphs whose underlying graphs are mating graphs, cf. A006024.
3
1, 1, 2, 8, 352, 32768, 9072896, 7389698048, 17695056717824, 124756911516516352, 2594584522679818518528, 159570269132472101976145920, 29103249711329178773313159168000, 15783921191009840333055992641622114304, 25514864105378775907711095288995558725779456
OFFSET
0,3
LINKS
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
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