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Consider the family of multigraphs enriched by the species of directed sets. Sequence gives number of those multigraphs with n labeled edges.
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%I #13 Jan 12 2021 19:51:12

%S 1,1,4,23,220,3016,55011,1265824,35496711,1183686987,46072834777,

%T 2062557088117,104926356851165,6004962409831577,383331023991407286,

%U 27094756978689827593,2107021273883402908850,179261681391054814324774,16602830645109035036038335

%N Consider the family of multigraphs enriched by the species of directed sets. 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="/A099692/b099692.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 A014500. - _Andrew Howroyd_, Jan 12 2021

%o (PARI) \\ R(n) is e.g.f. of 1,1,2,2,2,2,...; EnrichedGnSeq defined in A098620.

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

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

%Y Cf. A000110, A014500, A098620, A099693, A099694, A099695.

%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