A098638 Consider the family of directed multigraphs enriched by the species of odd sets. Sequence gives number of those multigraphs with n labeled loops and arcs.

1, 2, 13, 164, 3127, 82600, 2845775, 122820136, 6446913953, 402413160952, 29343933156485, 2464029760993520, 235446319553848087, 25346231173047308256, 3047931031445529965527, 406412844141860523543392, 59704680455100785101683457, 9608818815170839730520275488

Offset

0,2

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..200

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

Formula

E.g.f.: exp(-1)*Sum_{n>=0}(1+sinh(x))^(n^2)/n!. - Vladeta Jovovic, Mar 04 2008

E.g.f.: B(sinh(x)) where B(x) is the e.g.f. of A014507. - Andrew Howroyd, Jan 12 2021

Prog

(PARI) \\ EnrichedGdlSeq defined in A098622.
EnrichedGdlSeq(sinh(x + O(x*x^20))) \\ Andrew Howroyd, Jan 12 2021

Crossrefs

Cf. A014507, A098622, A098636, A098637, A098639.

Sequence in context: A132614 A187927 A252766 * A090643 A132521 A380772

Adjacent sequences: A098635 A098636 A098637 * A098639 A098640 A098641

Keyword

nonn

Author

N. J. A. Sloane, Oct 26 2004

Extensions

Missing a(10) inserted and terms a(13) and beyond from Andrew Howroyd, Jan 12 2021

Status

approved