A099695 -id:A099695 - cp's OEIS frontend

A099692 Consider the family of multigraphs enriched by the species of directed sets. Sequence gives number of those multigraphs with n labeled edges.

1, 1, 4, 23, 220, 3016, 55011, 1265824, 35496711, 1183686987, 46072834777, 2062557088117, 104926356851165, 6004962409831577, 383331023991407286, 27094756978689827593, 2107021273883402908850, 179261681391054814324774, 16602830645109035036038335

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. A000110, A014500, A098620, A099693, A099694, A099695.

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

E.g.f.: B(2*exp(x) - x - 2) where B(x) is the e.g.f. of A014500. - Andrew Howroyd, Jan 12 2021

Terms a(11) and beyond from Andrew Howroyd, Jan 12 2021

A099694 Consider the family of directed multigraphs enriched by the species of directed sets. Sequence gives number of those multigraphs with n labeled loops and arcs.

Original entry on oeis.org

1, 2, 17, 244, 5283, 156092, 5954547, 282221828, 16159327961, 1094056231572, 86116276633357, 7773114989571400, 795480206815177651, 91417037615848058160, 11701283925663217478843, 1656436690705751478232180, 257730676653629520748175377, 43837005194184348815823808500

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. A014507, A098622, A099692, A099693, A099695.

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

E.g.f.: B(2*exp(x) - x - 2) where B(x) is the e.g.f. of A014507. - Andrew Howroyd, Jan 12 2021

Terms a(11) and beyond from Andrew Howroyd, Jan 12 2021

cp's OEIS Frontend

A099692 Consider the family of multigraphs enriched by the species of directed sets. Sequence gives number of those multigraphs with n labeled edges.

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