cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A099718 Consider the family of directed multigraphs enriched by the species of trees. Sequence gives number of those multigraphs with n labeled loops and edges.

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