A099708 - OEIS

%I #13 Jan 12 2021 20:48:11

%S 1,1,6,60,854,16029,378871,10926690,375538541,15097900582,

%T 699359781567,36859422340308,2187121403805853,144804645827958839,

%U 10615679263174481480,856040905847508506792,75495130803739278866508,7244702305184037575057831,753093536414613689614872227

%N Consider the family of multigraphs enriched by the species of endofunctions. 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="/A099708/b099708.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 A000312. - _Andrew Howroyd_, Jan 12 2021

%o (PARI) \\ R(n) is A000312 as e.g.f.; EnrichedGnSeq defined in A098620.

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

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

%Y Cf. A000312, A014500, A098620, A099709, A099710, A099711.

%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