A099704 - OEIS

%I #12 Jan 12 2021 20:47:49

%S 1,2,24,776,79840,35397440,69619053504,564929183555840,

%T 18464894708236907776,2418517115222622481308160,

%U 1267747370909677813160722947072,2658511777246500251150215101758228480,22300872810108738542496498718468714032205824

%N Consider the family of multigraphs enriched by the species of directed graphs. Sequence gives number of those multigraphs with n labeled edges.

%D G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004.

%H Andrew Howroyd, <a href="/A099704/b099704.txt">Table of n, a(n) for n = 0..50</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 A014500 and 1 + R(x) is the e.g.f. of A002416. - _Andrew Howroyd_, Jan 12 2021

%o (PARI) \\ R(n) is A002416 as e.g.f.; EnrichedGnSeq defined in A098620.

%o R(n)={sum(k=0, n, 2^(k^2)*x^k/k!) + O(x*x^n)}

%o EnrichedGnSeq(R(15)) \\ _Andrew Howroyd_, Jan 12 2021

%Y Cf. A002416, A014500, A098620, A099705, A099706, A099707.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Oct 26 2004

%E Terms a(10) and beyond from _Andrew Howroyd_, Jan 12 2021