cp's OEIS Frontend

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

%I A102597 #9 Jan 20 2024 13:52:39
%S A102597 1,1,2,8,352,32768,9072896,7389698048,17695056717824,
%T A102597 124756911516516352,2594584522679818518528,
%U A102597 159570269132472101976145920,29103249711329178773313159168000,15783921191009840333055992641622114304,25514864105378775907711095288995558725779456
%N A102597 Number of n-node labeled connected oriented graphs whose underlying graphs are mating graphs, cf. A006024.
%H A102597 Andrew Howroyd, <a href="/A102597/b102597.txt">Table of n, a(n) for n = 0..50</a>
%F A102597 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
%o A102597 (PARI) \\ b(n) is A102596(n); permcount, edges defined in A369283.
%o A102597 b(n) = {my(s=0); forpart(p=n, s += permcount(p)*(-1)^(n-#p)*edges(p, w->1 + 2^w)); s}
%o A102597 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
%Y A102597 Cf. A006024, A102580 (digraphs), A102596 (not necessarily connected), A102599 (unlabeled), A369283.
%K A102597 nonn
%O A102597 0,3
%A A102597 Goran Kilibarda, Zoran Maksimovic, _Vladeta Jovovic_, Jan 22 2005
%E A102597 a(0)=1 prepended and a(13) onwards from _Andrew Howroyd_, Jan 20 2024