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Consider the family of directed multigraphs enriched by the species of parts. Sequence gives number of those multigraphs with n labeled loops and arcs
1, 4, 60, 1624, 66240, 3711200, 269670208, 24435113216, 2682916389632, 349223324753408, 52965538033020928, 9229753832340117504, 1826647528631522463744, 406579171521484851396608, 100934277604965329345822720, 27746271707522968205726416896
Andrew Howroyd, <a href="/A098630/b098630.txt">Table of n, a(n) for n = 0..100</a>
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
Terms a(11) and beyond from Andrew Howroyd, Jan 12 2021
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G. Paquin, <a href="/A038205/a038205.pdf">Dénombrement de multigraphes enrichis</a>, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004. [Cached copy, with permission]
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G. Paquin, D\'enombrement Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004.
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G. Paquin, D\'enombrement de multigraphes enrichis, M\'emoire, Mémoire, Math. Dept., Univ. Qu\'ebec \`a Montr\'eal, Québec à Montréal, 2004.
a(n) = 2^n*Bell(2*n). - _Vladeta Jovovic (vladeta(AT)eunet.rs), _, Aug 22 2006
_N. J. A. Sloane (njas(AT)research.att.com), _, Oct 26 2004