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.

A099716 Consider the family of multigraphs enriched by the species of trees. Sequence gives number of those multigraphs with n labeled edges.

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%I A099716 #12 Jan 12 2021 21:32:27
%S A099716 1,1,3,18,170,2244,38686,834594,21874433,681399298,24797467947,
%T A099716 1039645748808,49632586028650,2671404673776080,160726892084432840,
%U A099716 10729582290405547592,789572236551678855603,63682341168165082629698,5600777517339868668401105
%N A099716 Consider the family of multigraphs enriched by the species of trees. Sequence gives number of those multigraphs with n labeled edges.
%D A099716 G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004.
%H A099716 Andrew Howroyd, <a href="/A099716/b099716.txt">Table of n, a(n) for n = 0..100</a>
%H A099716 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 A099716 E.g.f.: B(R(x)) where B(x) is the e.g.f. of A014500 and 1 + R(x) is the e.g.f. of A000272. - _Andrew Howroyd_, Jan 12 2021
%o A099716 (PARI) \\ R(n) is A000272 as e.g.f.; EnrichedGnSeq defined in A098620.
%o A099716 R(n)={my(w=lambertw(-x + O(x*x^n))); 1 - w - w^2/2}
%o A099716 EnrichedGnSeq(R(20)) \\ _Andrew Howroyd_, Jan 12 2021
%Y A099716 Cf. A000272, A014500, A098620, A099717, A099718, A099719.
%K A099716 nonn
%O A099716 0,3
%A A099716 _N. J. A. Sloane_, Oct 26 2004
%E A099716 Terms a(12) and beyond from _Andrew Howroyd_, Jan 12 2021