A099712 Consider the family of multigraphs enriched by the species of arborescences. Sequence gives number of those multigraphs with n labeled edges.

1, 1, 4, 30, 338, 5169, 101251, 2446806, 71043973, 2429762734, 96364601877, 4375603494478, 225044659552381, 12990629618136191, 834981228656630494, 59346659738963806022, 4635924974380060251228, 395864230878802130389079, 36773114396103232927777067

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 R(x) is the e.g.f. of A000169. - Andrew Howroyd, Jan 12 2021

Prog

(PARI) \\ R(n) is A000169 as e.g.f.; EnrichedGnSeq defined in A098620.
R(n)={-lambertw(-x + O(x*x^n))}
EnrichedGnSeq(R(20)) \\ Andrew Howroyd, Jan 12 2021

Crossrefs

Cf. A000169, A014500, A098620, A099713, A099714, A099715.

Sequence in context: A121413 A001761 A292220 * A370931 A209440 A052316

Adjacent sequences: A099709 A099710 A099711 * A099713 A099714 A099715

Keyword

nonn

Author

N. J. A. Sloane, Oct 26 2004

Extensions

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

Status

approved