A050535 Number of loopless multigraphs on infinite set of nodes with n edges.
1, 1, 3, 8, 23, 66, 212, 686, 2389, 8682, 33160, 132277, 550835, 2384411, 10709827, 49782637, 238998910, 1182772364, 6023860266, 31525780044, 169316000494, 932078457785, 5253664040426, 30290320077851, 178480713438362, 1073918172017297
Offset: 0
Keywords
Examples
From _Gus Wiseman_, Jul 18 2018: (Start)
Non-isomorphic representatives of the a(3) = 8 set multipartitions of {1, 1, 2, 2, 3, 3}:
(123)(123)
(1)(23)(123)
(12)(13)(23)
(1)(1)(23)(23)
(1)(2)(3)(123)
(1)(2)(13)(23)
(1)(1)(2)(3)(23)
(1)(1)(2)(2)(3)(3)
(End)
References
- Frank Harary and Edgar M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 88, Eq. (4.1.18).
Links
- Andrew Howroyd, Table of n, a(n) for n = 0..50
- George Barnes, Sanjaye Ramgoolam, and Michael Stephanou, Permutation invariant Gaussian matrix models for financial correlation matrices, arXiv:2306.04569 [q-fin.ST], 2023.
- Frank Harary, The number of linear, directed, rooted, and connected graphs, Trans. Am. Math. Soc. 78 (1955) 445-463, eq. (24).
- Vladeta Jovovic, Number of m-rowed binary matrices with all row sums equal to n, up to row and column permutation
- 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.
Crossrefs
Programs
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Mathematica
seq[n_] := G[2n, x+O[x]^n, {}] // CoefficientList[#, x]&; seq[15] (* Jean-François Alcover, Dec 02 2020, using Andrew Howroyd's code for G in A339065 *)
Formula
Euler transform of A076864. - Andrew Howroyd, Oct 23 2019
Extensions
More terms from Sean A. Irvine, Oct 02 2011
Comments