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A053419
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Number of graphs with loops (symmetric relations) with n edges.
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12
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1, 2, 5, 14, 38, 107, 318, 972, 3111, 10410, 36371, 132656, 504636, 1998361, 8224448, 35112342, 155211522, 709123787, 3342875421, 16234342515, 81102926848, 416244824068, 2192018373522, 11831511359378, 65387590986455, 369661585869273, 2135966349269550, 12604385044890628
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OFFSET
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0,2
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COMMENTS
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In a multiset partition, two vertices are equivalent if in every block the multiplicity of the first is equal to the multiplicity of the second. a(n) is the number of non-isomorphic multiset partitions of {1, 1, 2, 2, 3, 3, ..., n, n} with no equivalent vertices. For example, non-isomorphic representatives of the a(2) = 5 multiset partitions are (1)(122), (11)(22), (1)(1)(22), (1)(2)(12), (1)(1)(2)(2). - Gus Wiseman, Jul 18 2018
a(n) is the number of unlabeled simple graphs with n edges rooted at one vertex. - Andrew Howroyd, Nov 22 2020
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LINKS
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FORMULA
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MATHEMATICA
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PROG
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seq(n)={my(A=O(x*x^n)); Vec(G(2*n, x+A, [1]))} \\ Andrew Howroyd, Nov 22 2020
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CROSSREFS
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Cf. A000664, A000666, A007716, A007717, A020555, A050535, A053419, A094574, A191970 (multisets), A316974, A339063.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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