A099710 Consider the family of directed multigraphs enriched by the species of endofunctions. Sequence gives number of those multigraphs with n labeled loops and arcs.
1, 2, 21, 372, 9503, 323528, 13976119, 740471952, 46918236113, 3486842393336, 299252510858253, 29285226572514608, 3233515108614711055, 399237909648934968160, 54699907257463871118015, 8261287679602024304387776, 1367355850924129919137226337, 246745297507913180076213875232
Offset: 0
Keywords
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]
Programs
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PARI
\\ R(n) is A000312 as e.g.f.; EnrichedGdlSeq defined in A098622. R(n)={1/(1 + lambertw(-x + O(x*x^n)))} EnrichedGdlSeq(R(20)) \\ Andrew Howroyd, Jan 12 2021
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 A000312. - Andrew Howroyd, Jan 12 2021
Extensions
Terms a(12) and beyond from Andrew Howroyd, Jan 12 2021