A099708 Consider the family of multigraphs enriched by the species of endofunctions. Sequence gives number of those multigraphs with n labeled edges.

1, 1, 6, 60, 854, 16029, 378871, 10926690, 375538541, 15097900582, 699359781567, 36859422340308, 2187121403805853, 144804645827958839, 10615679263174481480, 856040905847508506792, 75495130803739278866508, 7244702305184037575057831, 753093536414613689614872227

Offset

0,3

References

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

Links

Andrew Howroyd, Table of n, a(n) for n = 0..100

G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004. [Cached copy, with permission]

Formula

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

Prog

(PARI) \\ R(n) is A000312 as e.g.f.; EnrichedGnSeq defined in A098620.
R(n)={1/(1 + lambertw(-x + O(x*x^n)))}
EnrichedGnSeq(R(20)) \\ Andrew Howroyd, Jan 12 2021

Crossrefs

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

Sequence in context: A066151 A339191 A000407 * A177191 A010040 A138379

Adjacent sequences: A099705 A099706 A099707 * A099709 A099710 A099711

Keyword

nonn

Author

N. J. A. Sloane, Oct 26 2004

Extensions

Terms a(12) and beyond from Andrew Howroyd, Jan 12 2021

Status

approved