OFFSET
0,3
COMMENTS
Also, a(n) is the number of n-rowed binary matrices with all row sums equal to 2, up to row and column permutation (see Jovovic's formula). Also, a(n) is the limit of A192517(m,n) as m grows. - Max Alekseyev, Oct 18 2017
Row sums of the triangle defined by the Multiset Transformation of A076864,
1 ;
0 1;
0 2 1;
0 5 2 1;
0 12 8 2 1;
0 33 22 8 2 1;
0 103 72 26 8 2 1;
0 333 229 87 26 8 2 1;
0 1183 782 295 92 26 8 2 1;
0 4442 2760 1036 315 92 26 8 2 1;
0 17576 10270 3735 1129 321 92 26 8 2 1;
0 72810 39770 13976 4117 1154 321 92 26 8 2 1;
0 314595 160713 54132 15547 4237 1161 321 92 26 8 2 1;
- R. J. Mathar, Jul 18 2017
Also the number of non-isomorphic set multipartitions (multisets of sets) of {1, 1, 2, 2, 3, 3, ..., n, n}. - Gus Wiseman, Jul 18 2018
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.
FORMULA
Euler transform of A076864. - Andrew Howroyd, Oct 23 2019
EXAMPLE
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)
MATHEMATICA
seq[n_] := G[2n, x+O[x]^n, {}] // CoefficientList[#, x]&;
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladeta Jovovic, Dec 29 1999
EXTENSIONS
More terms from Sean A. Irvine, Oct 02 2011
STATUS
approved