A098631 Consider the family of directed multigraphs enriched by the species of parts. Sequence gives number of those multigraphs with n labeled arcs.

1, 2, 28, 696, 26512, 1402656, 97017792, 8418174848, 889241719040, 111774837350912, 16420543334734848, 2778708477919836160, 535183812199464341504, 116142946557502449852416, 28156854547845767203373056, 7569375509914847295271043072, 2241898693518356603925445017600

Offset: 0

Author

N. J. A. Sloane, Oct 26 2004

Keywords

• nonn

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]

Crossrefs

Cf. A000079, A014505, A020556, A098623, A098628, A098629, A098630.

Programs

PARI

\\ R(n) is A000079 as e.g.f.; EnrichedGdSeq defined in A098623.
R(n)={exp(2*x + O(x*x^n))}
EnrichedGdSeq(R(20)) \\ Andrew Howroyd, Jan 12 2021

Formula

a(n) = 2^n*A020556(n). - Vladeta Jovovic, Aug 11 2005

E.g.f.: B(R(x)) where B(x) is the e.g.f. of A014505 and 1 + R(x) is the e.g.f. of A000079. - Andrew Howroyd, Jan 12 2021

Extensions

More terms from Vladeta Jovovic, Aug 11 2005

Terms a(14) and beyond from Andrew Howroyd, Jan 12 2021