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A098630 Consider the family of directed multigraphs enriched by the species of parts. Sequence gives number of those multigraphs with n labeled loops and arcs 3
1, 4, 60, 1624, 66240, 3711200, 269670208, 24435113216, 2682916389632, 349223324753408, 52965538033020928, 9229753832340117504, 1826647528631522463744, 406579171521484851396608, 100934277604965329345822720, 27746271707522968205726416896 (list; graph; refs; listen; history; text; internal format)



G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004.


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]


a(n) = 2^n*Bell(2*n). - Vladeta Jovovic, Aug 22 2006

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 A000079. - Andrew Howroyd, Jan 12 2021


(PARI) a(n) = {2^n*sum(k=0, 2*n, stirling(2*n, k, 2))} \\ Andrew Howroyd, Jan 12 2021

(PARI) \\ R(n) is A000079 as e.g.f.; EnrichedGdlSeq defined in A098622.

R(n)={exp(2*x + O(x*x^n))}

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


Cf. A000079, A014507, A098622, A098628, A098629, A098631.

Sequence in context: A013484 A013485 A324959 * A336637 A330069 A211309

Adjacent sequences:  A098627 A098628 A098629 * A098631 A098632 A098633




N. J. A. Sloane, Oct 26 2004


Terms a(11) and beyond from Andrew Howroyd, Jan 12 2021



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Last modified November 30 13:47 EST 2021. Contains 349420 sequences. (Running on oeis4.)