A099706 Consider the family of directed multigraphs enriched by the species of directed graphs. Sequence gives number of those multigraphs with n labeled loops and arcs.

1, 4, 84, 3568, 305712, 87782720, 144600947392, 1139235294403328, 37012349010095737088, 4840037457225169875031040, 2535930555678883610642223895552, 5317274645187046706095607711946092544, 44602319906972740832371696997145322907873280

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..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 A014507 and 1 + R(x) is the e.g.f. of A002416. - Andrew Howroyd, Jan 12 2021

Prog

(PARI) \\ R(n) is A002416 as e.g.f.; EnrichedGdlSeq defined in A098622.
R(n)={sum(k=0, n, 2^(k^2)*x^k/k!) + O(x*x^n)}
EnrichedGdlSeq(R(15)) \\ Andrew Howroyd, Jan 12 2021

Crossrefs

Cf. A002416, A014507, A098622, A099704, A099705, A099707.

Sequence in context: A357672 A361542 A024260 * A012065 A012139 A012037

Adjacent sequences: A099703 A099704 A099705 * A099707 A099708 A099709

Keyword

nonn

Author

N. J. A. Sloane, Oct 26 2004

Extensions

Terms a(10) and beyond from Andrew Howroyd, Jan 12 2021

Status

approved