A099702 - OEIS

%I #12 Jan 12 2021 21:31:47

%S 1,2,17,256,5719,173446,6768075,328288840,19468007553,1458080017522,

%T 183476204746761,87209577493989776,154656821805639801687,

%U 617619828457724835488214,5008102331929281541386123923,81618549234469098721106601012472,2666950050438611111026601803629686849

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

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

%H Andrew Howroyd, <a href="/A099702/b099702.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 A014507 and 1 + R(x) is the e.g.f. of A006125. - _Andrew Howroyd_, Jan 12 2021

%o (PARI) \\ R(n) is A006125 as e.g.f.; EnrichedGdlSeq defined in A098622.

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

%o EnrichedGdlSeq(R(20)) \\ _Andrew Howroyd_, Jan 12 2021

%Y Cf. A006125, A014507, A098622, A099700, A099701, A099703.

%K nonn

%O 0,2

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

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