A099694 - OEIS

%I #12 Jan 12 2021 21:30:51

%S 1,2,17,244,5283,156092,5954547,282221828,16159327961,1094056231572,

%T 86116276633357,7773114989571400,795480206815177651,

%U 91417037615848058160,11701283925663217478843,1656436690705751478232180,257730676653629520748175377,43837005194184348815823808500

%N Consider the family of directed multigraphs enriched by the species of directed sets. 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="/A099694/b099694.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 A014507. - _Andrew Howroyd_, Jan 12 2021

%o (PARI) \\ R(n) is e.g.f. of 1, 1, 2, 2, 2, ...; EnrichedGdlSeq defined in A098622.

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

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

%Y Cf. A014507, A098622, A099692, A099693, A099695.

%K nonn

%O 0,2

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

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