A098639 -id:A098639 - cp's OEIS frontend

A098636 Consider the family of multigraphs enriched by the species of odd sets. Sequence gives number of those multigraphs with n labeled edges.

1, 1, 2, 10, 78, 885, 13487, 261848, 6255453, 179297990, 6046396379, 236175330388, 10549286540957, 533103416306743, 30203144498636380, 1903491404510540902, 132543022174482851436, 10136316177816553484295, 846893706267135762556915, 76941424170126460702604994

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..200
G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004. [Cached copy, with permission]

Cf. A014500, A098620, A098637, A098638, A098639.

\\ EnrichedGnSeq defined in A098620.
EnrichedGnSeq(sinh(x + O(x*x^20))) \\ Andrew Howroyd, Jan 12 2021

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

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

A098638 Consider the family of directed multigraphs enriched by the species of odd sets. Sequence gives number of those multigraphs with n labeled loops and arcs.

Original entry on oeis.org

1, 2, 13, 164, 3127, 82600, 2845775, 122820136, 6446913953, 402413160952, 29343933156485, 2464029760993520, 235446319553848087, 25346231173047308256, 3047931031445529965527, 406412844141860523543392, 59704680455100785101683457, 9608818815170839730520275488

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..200
G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004. [Cached copy, with permission]

Cf. A014507, A098622, A098636, A098637, A098639.

\\ EnrichedGdlSeq defined in A098622.
EnrichedGdlSeq(sinh(x + O(x*x^20))) \\ Andrew Howroyd, Jan 12 2021

E.g.f.: exp(-1)*Sum_{n>=0}(1+sinh(x))^(n^2)/n!. - Vladeta Jovovic, Mar 04 2008

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

Missing a(10) inserted and terms a(13) and beyond from Andrew Howroyd, Jan 12 2021

cp's OEIS Frontend

A098636 Consider the family of multigraphs enriched by the species of odd sets. Sequence gives number of those multigraphs with n labeled edges.

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