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A098623 Consider the family of directed multigraphs enriched by the species of set partitions. Sequence gives number of those multigraphs with n labeled arcs. 8
1, 1, 8, 109, 2229, 62684, 2289151, 104344153, 5767234550, 378073098155, 28888082263581, 2536660090249102, 253007765488793325, 28383529110762969901, 3551558435250676339536, 492092920443604792460905, 75025155137863150912784409, 12516480979952118669729618300 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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. Labelle, Counting enriched multigraphs according to the number of their edges (or arcs), Discrete Math., 217 (2000), 237-248.

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 A014505 and 1 + R(x) is the e.g.f. of A000110. - Andrew Howroyd, Jan 12 2021

PROG

(PARI) \\ here R(n) is A000110 as e.g.f.

egfA020556(n)={my(bell=serlaplace(exp(exp(x + O(x^(2*n+1)))-1))); sum(i=0, n, sum(k=0, i, (-1)^k*binomial(i, k)*polcoef(bell, 2*i-k))*x^i/i!) + O(x*x^n)}

EnrichedGdSeq(R)={my(n=serprec(R, x)-1, B=subst(egfA020556(n), x, log(1+x + O(x*x^n)))); Vec(serlaplace(subst(B, x, R-polcoef(R, 0))))}

R(n)={exp(exp(x + O(x*x^n))-1)}

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

CROSSREFS

Cf. A000110, A098620, A098621, A098622.

Sequence in context: A259233 A322718 A309188 * A297971 A076151 A020560

Adjacent sequences:  A098620 A098621 A098622 * A098624 A098625 A098626

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 May 16 21:28 EDT 2021. Contains 343951 sequences. (Running on oeis4.)