A099695 - OEIS

%I #13 Jan 13 2021 01:21:36

%S 1,1,8,106,2144,59844,2173450,98648246,5433864078,355229741266,

%T 27080154837658,2373310690810690,236327564463489838,

%U 26475199136060717618,3308794737926514931894,457980967372496137472590,69761664006643652403884218,11629282648335699139979015070

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

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

%H Andrew Howroyd, <a href="/A099695/b099695.txt">Table of n, a(n) for n = 0..100</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(2*exp(x) - x - 2) where B(x) is the e.g.f. of A014505. - _Andrew Howroyd_, Jan 12 2021

%o (PARI) \\ R(n) is e.g.f. of 1, 1, 2, 2, 2, ...; EnrichedGdSeq defined in A098623.

%o R(n)={2*exp(x + O(x*x^n)) - x - 1}

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

%Y Cf. A014505, A098623, A099692, A099693, A099694.

%K nonn

%O 0,3

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

%E Terms a(11) and beyond from _Andrew Howroyd_, Jan 12 2021