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.

A099714 Consider the family of directed multigraphs enriched by the species of arborescences. Sequence gives number of those multigraphs with n labeled loops and arcs.

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%I A099714 #12 Jan 12 2021 21:32:19
%S A099714 1,2,17,258,5771,174528,6770119,324895980,18781627193,1281239711000,
%T A099714 101465766593553,9204346831406488,945843113150930899,
%U A099714 109072242262950463552,14001689466624210245831,1986950788160317182000976,309800790825415866952825137,52786928631190620809803203872
%N A099714 Consider the family of directed multigraphs enriched by the species of arborescences. Sequence gives number of those multigraphs with n labeled loops and arcs.
%D A099714 G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004.
%H A099714 Andrew Howroyd, <a href="/A099714/b099714.txt">Table of n, a(n) for n = 0..100</a>
%H A099714 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 A099714 E.g.f.: B(R(x)) where B(x) is the e.g.f. of A014507 and R(x) is the e.g.f. of A000169. - _Andrew Howroyd_, Jan 12 2021
%o A099714 (PARI) \\ R(n) is A000169 as e.g.f.; EnrichedGdlSeq defined in A098622.
%o A099714 R(n)={-lambertw(-x + O(x*x^n))}
%o A099714 EnrichedGdlSeq(R(20)) \\ _Andrew Howroyd_, Jan 12 2021
%Y A099714 Cf. A000169, A014507, A098622, A099712, A099713, A099715.
%K A099714 nonn
%O A099714 0,2
%A A099714 _N. J. A. Sloane_, Oct 26 2004
%E A099714 Terms a(12) and beyond from _Andrew Howroyd_, Jan 12 2021