A099713 -id:A099713 - cp's OEIS frontend

A099712 Consider the family of multigraphs enriched by the species of arborescences. Sequence gives number of those multigraphs with n labeled edges.

1, 1, 4, 30, 338, 5169, 101251, 2446806, 71043973, 2429762734, 96364601877, 4375603494478, 225044659552381, 12990629618136191, 834981228656630494, 59346659738963806022, 4635924974380060251228, 395864230878802130389079, 36773114396103232927777067

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. A000169, A014500, A098620, A099713, A099714, A099715.

\\ R(n) is A000169 as e.g.f.; EnrichedGnSeq defined in A098620.
R(n)={-lambertw(-x + O(x*x^n))}
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 R(x) is the e.g.f. of A000169. - Andrew Howroyd, Jan 12 2021

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

A099714 Consider the family of directed multigraphs enriched by the species of arborescences. Sequence gives number of those multigraphs with n labeled loops and arcs.

Original entry on oeis.org

1, 2, 17, 258, 5771, 174528, 6770119, 324895980, 18781627193, 1281239711000, 101465766593553, 9204346831406488, 945843113150930899, 109072242262950463552, 14001689466624210245831, 1986950788160317182000976, 309800790825415866952825137, 52786928631190620809803203872

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. A000169, A014507, A098622, A099712, A099713, A099715.

\\ R(n) is A000169 as e.g.f.; EnrichedGdlSeq defined in A098622.
R(n)={-lambertw(-x + O(x*x^n))}
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 R(x) is the e.g.f. of A000169. - Andrew Howroyd, Jan 12 2021

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

cp's OEIS Frontend

A099712 Consider the family of multigraphs enriched by the species of arborescences. Sequence gives number of those multigraphs with n labeled edges.

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