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A265580
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Number of (unlabeled) loopless multigraphs with no isolated vertices such that the sum of the numbers of vertices and edges is n.
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3
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1, 0, 0, 1, 1, 2, 4, 7, 13, 27, 54, 112, 243, 538, 1223, 2875, 6909, 17052, 43138, 111686, 295658, 799684, 2207356, 6213391, 17820961, 52042771, 154640528, 467254731, 1434837672, 4475520062, 14173115724, 45548395180, 148485883443, 490831193397, 1644581336531
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OFFSET
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0,6
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COMMENTS
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Also the number of skeletal 2-cliquish graphs with n vertices and no isolated vertices. See Einstein et al. link below.
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LINKS
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D. Einstein, M. Farber, E. Gunawan, M. Joseph, M. Macauley, J. Propp and S. Rubinstein-Salzedo, Noncrossing partitions, toggles, and homomesies, arXiv:1510.06362 [math.CO], 2015.
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FORMULA
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EXAMPLE
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For n = 5, the a(5) = 2 such multigraphs are the graph with three vertices and edges from one vertex to each of the other two, and the graph with two vertices connected by three edges.
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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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