A099696 -id:A099696 - cp's OEIS frontend

A099698 Consider the family of directed multigraphs enriched by the species of involutions. Sequence gives number of those multigraphs with n labeled loops and arcs.

1, 2, 17, 248, 5403, 160420, 6142567, 291996934, 16759322733, 1136940595762, 89641455771637, 8102778995663368, 830222723124364047, 95509354134959796556, 12236166882713532940611, 1733521075683722202738222, 269910543278748394820341769, 45936441912756036235229989058

Offset: 0

N. J. A. Sloane, Jun 25 2017

nonn

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. A000085, A014507, A098622, A099696, A099697, A099699.

\\ R(n) is A000085 as e.g.f.; EnrichedGdlSeq defined in A098622.
R(n)={exp(x+x^2/2 + 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 1 + R(x) is the e.g.f. of A000085. - Andrew Howroyd, Jan 12 2021

Dead sequence restored, corrected and extended by Andrew Howroyd, Jan 12 2021

A099699 Consider the family of directed multigraphs enriched by the species of involutions. Sequence gives number of those multigraphs with n labeled arcs.

Original entry on oeis.org

1, 1, 8, 108, 2200, 61708, 2249268, 102377404, 5651999688, 370171228504, 28262385542832, 2480108374814480, 247231765611893504, 27722619251007202720, 3467475213036160205984, 480277499859342401636704, 73202023124111697153718080, 12209186681659842887207280448

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. A000085, A014505, A098623, A099696, A099697, A099698.

\\ 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

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

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

cp's OEIS Frontend

A099698 Consider the family of directed multigraphs enriched by the species of involutions. Sequence gives number of those multigraphs with n labeled loops and arcs.

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