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.

A099706 Consider the family of directed multigraphs enriched by the species of directed graphs. Sequence gives number of those multigraphs with n labeled loops and arcs.

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%I A099706 #12 Jan 12 2021 21:32:02
%S A099706 1,4,84,3568,305712,87782720,144600947392,1139235294403328,
%T A099706 37012349010095737088,4840037457225169875031040,
%U A099706 2535930555678883610642223895552,5317274645187046706095607711946092544,44602319906972740832371696997145322907873280
%N A099706 Consider the family of directed multigraphs enriched by the species of directed graphs. Sequence gives number of those multigraphs with n labeled loops and arcs.
%D A099706 G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004.
%H A099706 Andrew Howroyd, <a href="/A099706/b099706.txt">Table of n, a(n) for n = 0..50</a>
%H A099706 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 A099706 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 A002416. - _Andrew Howroyd_, Jan 12 2021
%o A099706 (PARI) \\ R(n) is A002416 as e.g.f.; EnrichedGdlSeq defined in A098622.
%o A099706 R(n)={sum(k=0, n, 2^(k^2)*x^k/k!) + O(x*x^n)}
%o A099706 EnrichedGdlSeq(R(15)) \\ _Andrew Howroyd_, Jan 12 2021
%Y A099706 Cf. A002416, A014507, A098622, A099704, A099705, A099707.
%K A099706 nonn
%O A099706 0,2
%A A099706 _N. J. A. Sloane_, Oct 26 2004
%E A099706 Terms a(10) and beyond from _Andrew Howroyd_, Jan 12 2021