A098630 -id:A098630 - cp's OEIS frontend

A098628 Consider the family of multigraphs enriched by the species of parts. Sequence gives number of those multigraphs with n labeled edges.

1, 2, 12, 128, 2224, 56000, 1880832, 79985792, 4161468928, 258415579648, 18793653411840, 1576791247634432, 150745211441983488, 16253127712884269056, 1959064946185017851904, 262002352633857351942144, 38624060984664180255621120, 6240304185636529522872025088

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. A000079, A014500, A098620, A098629, A098630, A098631.

\\ R(n) is A000079 as e.g.f.; EnrichedGnSeq defined in A098620.
R(n)={exp(2*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 1 + R(x) is the e.g.f. of A000079. - Andrew Howroyd, Jan 12 2021

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

A098631 Consider the family of directed multigraphs enriched by the species of parts. Sequence gives number of those multigraphs with n labeled arcs.

Original entry on oeis.org

1, 2, 28, 696, 26512, 1402656, 97017792, 8418174848, 889241719040, 111774837350912, 16420543334734848, 2778708477919836160, 535183812199464341504, 116142946557502449852416, 28156854547845767203373056, 7569375509914847295271043072, 2241898693518356603925445017600

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. A000079, A014505, A020556, A098623, A098628, A098629, A098630.

\\ R(n) is A000079 as e.g.f.; EnrichedGdSeq defined in A098623.
R(n)={exp(2*x + O(x*x^n))}
EnrichedGdSeq(R(20)) \\ Andrew Howroyd, Jan 12 2021

a(n) = 2^n*A020556(n). - Vladeta Jovovic, Aug 11 2005

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 A000079. - Andrew Howroyd, Jan 12 2021

More terms from Vladeta Jovovic, Aug 11 2005

Terms a(14) and beyond from Andrew Howroyd, Jan 12 2021

cp's OEIS Frontend

A098628 Consider the family of multigraphs enriched by the species of parts. Sequence gives number of those multigraphs with n labeled edges.

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