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A050535
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Number of loopless multigraphs on infinite set of nodes with n edges.
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46
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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
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OFFSET
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0,3
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COMMENTS
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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;
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
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REFERENCES
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Frank Harary and Edgar M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 88, Eq. (4.1.18).
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LINKS
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FORMULA
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EXAMPLE
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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)
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MATHEMATICA
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seq[n_] := G[2n, x+O[x]^n, {}] // CoefficientList[#, x]&;
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CROSSREFS
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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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