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A099699
Consider the family of directed multigraphs enriched by the species of involutions. Sequence gives number of those multigraphs with n labeled arcs.
3
1, 1, 8, 108, 2200, 61708, 2249268, 102377404, 5651999688, 370171228504, 28262385542832, 2480108374814480, 247231765611893504, 27722619251007202720, 3467475213036160205984, 480277499859342401636704, 73202023124111697153718080, 12209186681659842887207280448
OFFSET
0,3
REFERENCES
G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004.
LINKS
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 A000085. - Andrew Howroyd, Jan 12 2021
PROG
(PARI) \\ R(n) is A000085 as e.g.f.; EnrichedGdSeq defined in A098623.
R(n)={exp(x+x^2/2 + O(x*x^n))}
EnrichedGdSeq(R(20)) \\ Andrew Howroyd, Jan 12 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Oct 26 2004
EXTENSIONS
Terms a(11) and beyond from Andrew Howroyd, Jan 12 2021
STATUS
approved