%I #12 Jan 12 2021 21:32:40
%S 1,2,15,207,4274,120698,4408714,200482089,11035845002,719691942986,
%T 54661283926338,4768412660292713,472309503983879356,
%U 52604316569196875434,6533611563916740388476,898472724512273277951811,135941600045496082012663932,22505828691354514668620263242
%N Consider the family of directed multigraphs enriched by the species of trees. Sequence gives number of those multigraphs with n labeled loops and edges.
%D G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004.
%H Andrew Howroyd, <a href="/A099718/b099718.txt">Table of n, a(n) for n = 0..100</a>
%H G. Paquin, <a href="/A038205/a038205.pdf">Dénombrement de multigraphes enrichis</a>, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004. [Cached copy, with permission]
%F E.g.f.: B(R(x)) where B(x) is the e.g.f. of A014507 and 1 + R(x) is the e.g.f. of A000272. - _Andrew Howroyd_, Jan 12 2021
%o (PARI) \\ R(n) is A000272 as e.g.f.; EnrichedGdlSeq defined in A098622.
%o R(n)={my(w=lambertw(-x + O(x*x^n))); 1 - w - w^2/2}
%o EnrichedGdlSeq(R(20)) \\ _Andrew Howroyd_, Jan 12 2021
%Y Cf. A000272, A014507, A098622, A099716, A099717, A099719.
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Oct 26 2004
%E Terms a(12) and beyond from _Andrew Howroyd_, Jan 12 2021