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A099702 Consider the family of directed multigraphs enriched by the species of simple graphs. Sequence gives number of those multigraphs with n labeled loops and arcs. 2
1, 2, 17, 256, 5719, 173446, 6768075, 328288840, 19468007553, 1458080017522, 183476204746761, 87209577493989776, 154656821805639801687, 617619828457724835488214, 5008102331929281541386123923, 81618549234469098721106601012472, 2666950050438611111026601803629686849 (list; graph; refs; listen; history; text; internal format)
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 A006125. - Andrew Howroyd, Jan 12 2021

PROG

(PARI) \\ R(n) is A006125 as e.g.f.; EnrichedGdlSeq defined in A098622.

R(n)={sum(k=0, n, 2^binomial(k, 2)*x^k/k!) + O(x*x^n)}

EnrichedGdlSeq(R(20)) \\ Andrew Howroyd, Jan 12 2021

CROSSREFS

Cf. A006125, A014507, A098622, A099700, A099701, A099703.

Sequence in context: A218681 A098622 A020561 * A253549 A002590 A029735

Adjacent sequences:  A099699 A099700 A099701 * A099703 A099704 A099705

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Oct 26 2004

EXTENSIONS

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

STATUS

approved

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Last modified September 20 05:24 EDT 2021. Contains 347577 sequences. (Running on oeis4.)