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%I #12 Jan 12 2021 21:32:27
%S 1,1,3,18,170,2244,38686,834594,21874433,681399298,24797467947,
%T 1039645748808,49632586028650,2671404673776080,160726892084432840,
%U 10729582290405547592,789572236551678855603,63682341168165082629698,5600777517339868668401105
%N Consider the family of multigraphs enriched by the species of trees. 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="/A099716/b099716.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(R(x)) where B(x) is the e.g.f. of A014500 and 1 + R(x) is the e.g.f. of A000272. - _Andrew Howroyd_, Jan 12 2021
%o (PARI) \\ R(n) is A000272 as e.g.f.; EnrichedGnSeq defined in A098620.
%o R(n)={my(w=lambertw(-x + O(x*x^n))); 1 - w - w^2/2}
%o EnrichedGnSeq(R(20)) \\ _Andrew Howroyd_, Jan 12 2021
%Y Cf. A000272, A014500, A098620, A099717, A099718, A099719.
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Oct 26 2004
%E Terms a(12) and beyond from _Andrew Howroyd_, Jan 12 2021
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