A053465 Number of connected 2-multigraphs on n nodes.

1, 1, 2, 7, 53, 712, 24576, 2275616, 589543159, 420188096140, 819411181635025, 4381819315336997184, 64583749250393921183423, 2638507778912832094660037006, 300397569392490080058575760090548, 95776592061550107555640978862165082446

Offset

0,3

Comments

A 2-multigraph is similar to an ordinary graph except there are 0, 1 or 2 edges between any two nodes (self-loops are not allowed).

Also the number of connected signed graphs on n unlabeled nodes. - Andrew Howroyd, Sep 25 2018

Links

Andrew Howroyd, Table of n, a(n) for n = 0..50

Edward A. Bender and E. Rodney Canfield, Enumeration of connected invariant graphs, Journal of Combinatorial Theory, Series B 34.3 (1983): 268-278. See p. 273.

Formula

Inverse Euler transform of A004102. - Andrew Howroyd, Sep 25 2018

Mathematica

A004102 = Import["https://oeis.org/A004102/b004102.txt", "Table"][[All, 2]];
(* EulerInvTransform is defined in A022562 *)
Join[{1}, EulerInvTransform[A004102 // Rest]] (* Jean-François Alcover, Sep 12 2019, after Andrew Howroyd, updated Mar 17 2020 *)

Crossrefs

Cf. A004102, A318590.

Sequence in context: A259530 A119772 A104084 * A193191 A180720 A168558

Adjacent sequences: A053462 A053463 A053464 * A053466 A053467 A053468

Keyword

easy,nonn

Author

Vladeta Jovovic, Jan 13 2000

Extensions

a(0)=1 prepended and terms a(15) and beyond from Andrew Howroyd, Sep 25 2018

Status

approved