A076864 Number of connected loopless multigraphs with n edges.

1, 1, 2, 5, 12, 33, 103, 333, 1183, 4442, 17576, 72810, 314595, 1410139, 6541959, 31322474, 154468852, 783240943, 4077445511, 21765312779, 118999764062, 665739100725, 3807640240209, 22246105114743, 132672322938379, 807126762251748

Offset: 0

Author

N. J. A. Sloane, Nov 23 2002

Keywords

• nonn
• easy

Comments

Inverse Euler transform of A050535.

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..50
• Patrick T. Komiske, Eric M. Metodiev, and Jesse Thaler, Energy flow polynomials: A complete linear basis for jet substructure, arXiv:1712.07124 [hep-ph], 2017.
• Tsuyoshi Miezaki, Akihiro Munemasa, Yusaku Nishimura, Tadashi Sakuma, and Shuhei Tsujie, Universal graph series, chromatic functions, and their index theory, arXiv:2403.09985 [math.CO], 2024. See p. 23.
• N. J. A. Sloane, Transforms
• Gus Wiseman, Non-isomorphic representatives of the unlabeled connected multigraphs counted by the first 5 terms

Crossrefs

Row sums of A191646.

Cf. A050535 (multisets), A076865, A076866, A076867.

Cf. A000664, A007718, A054923, A191970, A275421, A317672, A322114, A322137, A322148.

Programs

Mathematica

A050535 = Cases[Import["https://oeis.org/A050535/b050535.txt", "Table"], {, }][[All, 2]];
(* EulerInvTransform is defined in A022562 *)
Join[{1}, EulerInvTransform[A050535 // Rest]] (* Jean-François Alcover, Feb 11 2020, updated Mar 17 2020 *)

Extensions

More terms from Sean A. Irvine, Oct 02 2011

Name and comment swapped by Gus Wiseman, Nov 28 2018

a(0)=1 prepended by Andrew Howroyd, Oct 23 2019