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

0,3

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

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 *)

Crossrefs

Row sums of A191646.

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

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

Sequence in context: A208957 A209051 A209216 * A209798 A196545 A032292

Adjacent sequences: A076861 A076862 A076863 * A076865 A076866 A076867

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 23 2002

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

Status

approved