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A099714 Consider the family of directed multigraphs enriched by the species of arborescences. Sequence gives number of those multigraphs with n labeled loops and arcs. 2
1, 2, 17, 258, 5771, 174528, 6770119, 324895980, 18781627193, 1281239711000, 101465766593553, 9204346831406488, 945843113150930899, 109072242262950463552, 14001689466624210245831, 1986950788160317182000976, 309800790825415866952825137, 52786928631190620809803203872 (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..100

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 R(x) is the e.g.f. of A000169. - Andrew Howroyd, Jan 12 2021

PROG

(PARI) \\ R(n) is A000169 as e.g.f.; EnrichedGdlSeq defined in A098622.

R(n)={-lambertw(-x + O(x*x^n))}

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

CROSSREFS

Cf. A000169, A014507, A098622, A099712, A099713, A099715.

Sequence in context: A029735 A291206 A037896 * A301584 A195443 A176585

Adjacent sequences:  A099711 A099712 A099713 * A099715 A099716 A099717

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 January 24 15:43 EST 2022. Contains 350540 sequences. (Running on oeis4.)