A099717 -id:A099717 - cp's OEIS frontend

A099716 Consider the family of multigraphs enriched by the species of trees. Sequence gives number of those multigraphs with n labeled edges.

1, 1, 3, 18, 170, 2244, 38686, 834594, 21874433, 681399298, 24797467947, 1039645748808, 49632586028650, 2671404673776080, 160726892084432840, 10729582290405547592, 789572236551678855603, 63682341168165082629698, 5600777517339868668401105

Offset: 0

N. J. A. Sloane, Oct 26 2004

nonn

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]

Cf. A000272, A014500, A098620, A099717, A099718, A099719.

\\ R(n) is A000272 as e.g.f.; EnrichedGnSeq defined in A098620.
R(n)={my(w=lambertw(-x + O(x*x^n))); 1 - w - w^2/2}
EnrichedGnSeq(R(20)) \\ Andrew Howroyd, Jan 12 2021

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 A000272. - Andrew Howroyd, Jan 12 2021

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

A099718 Consider the family of directed multigraphs enriched by the species of trees. Sequence gives number of those multigraphs with n labeled loops and edges.

Original entry on oeis.org

1, 2, 15, 207, 4274, 120698, 4408714, 200482089, 11035845002, 719691942986, 54661283926338, 4768412660292713, 472309503983879356, 52604316569196875434, 6533611563916740388476, 898472724512273277951811, 135941600045496082012663932, 22505828691354514668620263242

Offset: 0

N. J. A. Sloane, Oct 26 2004

nonn

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]

Cf. A000272, A014507, A098622, A099716, A099717, A099719.

\\ R(n) is A000272 as e.g.f.; EnrichedGdlSeq defined in A098622.
R(n)={my(w=lambertw(-x + O(x*x^n))); 1 - w - w^2/2}
EnrichedGdlSeq(R(20)) \\ Andrew Howroyd, Jan 12 2021

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 A000272. - Andrew Howroyd, Jan 12 2021

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

cp's OEIS Frontend

A099716 Consider the family of multigraphs enriched by the species of trees. Sequence gives number of those multigraphs with n labeled edges.

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