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A060516
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Number of series-reduced (or homeomorphically irreducible) graphs with loops on n labeled nodes.
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12
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1, 1, 5, 26, 328, 9700, 711836, 111817032, 35130791054, 21495893690664, 25409892375220474, 58052821046020873856, 257486314335782707924088, 2230295461268044025586193298, 37948847404292424846290915818844
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OFFSET
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0,3
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COMMENTS
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Conjecture: the number of connected graphs of this type is 1, 1, 4, 13, 203, 7754, ... (n>=0). - R. J. Mathar, Apr 29 2019
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REFERENCES
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I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, John Wiley and Sons, N.Y., 1983.
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LINKS
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FORMULA
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E.g.f. : (1 + x)^( - 1/2) * exp( - x/2 - x^2/4) * Sum_{k=0..inf} 2^binomial(k + 1, 2) * exp( - x * k^2/(2 * (1 + x)) + x * k/2) * x^k/k!.
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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