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Search: id:A020554
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| A020554 |
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Number of multigraphs on n labeled edges (without loops). |
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+0
9
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| 1, 1, 3, 16, 139, 1750, 29388, 624889, 16255738, 504717929, 18353177160, 769917601384, 36803030137203, 1984024379014193, 119571835094300406, 7995677265437541258, 589356399302126773920
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Or, number of bicoverings of an n-set.
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REFERENCES
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Comtet, L.; Birecouvrements et birevetements d'un ensemble fini. Studia Sci. Math. Hungar. 3 1968 137-152.
G. Labelle, Counting enriched multigraphs..., Discrete Math., 217 (2000), 237-248.
G. Paquin, D\'enombrement de multigraphes enrichis, M\'emoire, Math. Dept., Univ. Qu\'ebec \`a Montr\'eal, 2004.
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FORMULA
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E.g.f.: exp(-3/2+exp(x)/2)*Sum(exp(binomial(n, 2)*x)/n!, n=0..infinity) [Comtet] - Vladeta Jovovic (vladeta(AT)Eunet.yu), Apr 27 2004
E.g.f. (an equivalent version in Maple format): G:=exp(-1+(exp(z)-1)/2)*sum(exp(s*(s-1)*z/2)/s!, s=0..infinity);
E.g.f.: exp((exp(x)-1)/2)*Sum(A020556(n)*(x/2)^n/n!, n=0..infinity). - Vladeta Jovovic (vladeta(AT)Eunet.yu), May 02 2004
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MATHEMATICA
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Ceiling[ CoefficientList[ Series[ Exp[ -1 + (Exp[ z ] - 1)/2 ]Sum[ Exp[ s(s - 1)z/2 ]/s!, {s, 0, 21} ], {z, 0, 9} ], z ] Table[ n!, {n, 0, 9} ] ]. - Mitch Harris, May 01 2004.
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CROSSREFS
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Cf. A002718, A020555.
Sequence in context: A135746 A006057 A002719 this_sequence A062874 A062873 A109398
Adjacent sequences: A020551 A020552 A020553 this_sequence A020555 A020556 A020557
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KEYWORD
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nonn,nice,easy
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AUTHOR
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Gilbert Labelle (gilbert(AT)lacim.uqam.ca), Simon Plouffe (plouffe(AT)math.uqam.ca)
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