A099700 Consider the family of multigraphs enriched by the species of simple graphs. Sequence gives number of those multigraphs with n labeled edges.

1, 1, 4, 29, 330, 5438, 128211, 4808964, 378829853, 77137284917, 36854103598061, 36864364745783295, 74684573193253556537, 304187997559381840229969, 2484431769481244742219110666, 40639512967159110848931023115111, 1330529956364528398902155692019721596

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..50

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 A006125. - Andrew Howroyd, Jan 12 2021

Prog

(PARI) \\ R(n) is A006125 as e.g.f.; EnrichedGnSeq defined in A098620.
R(n)={sum(k=0, n, 2^binomial(k, 2)*x^k/k!) + O(x*x^n)}
EnrichedGnSeq(R(20)) \\ Andrew Howroyd, Jan 12 2021

Crossrefs

Cf. A006125, A014500, A098620, A099701, A099702, A099703.

Sequence in context: A028853 A118795 A325478 * A305636 A276728 A256006

Adjacent sequences: A099697 A099698 A099699 * A099701 A099702 A099703

Keyword

nonn

Author

N. J. A. Sloane, Oct 26 2004

Extensions

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

Status

approved