A099708 Consider the family of multigraphs enriched by the species of endofunctions. Sequence gives number of those multigraphs with n labeled edges.
1, 1, 6, 60, 854, 16029, 378871, 10926690, 375538541, 15097900582, 699359781567, 36859422340308, 2187121403805853, 144804645827958839, 10615679263174481480, 856040905847508506792, 75495130803739278866508, 7244702305184037575057831, 753093536414613689614872227
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
-
PARI
\\ R(n) is A000312 as e.g.f.; EnrichedGnSeq defined in A098620. R(n)={1/(1 + lambertw(-x + O(x*x^n)))} EnrichedGnSeq(R(20)) \\ Andrew Howroyd, Jan 12 2021
Formula
E.g.f.: B(R(x)) where B(x) is the e.g.f. of A014500 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