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A297474
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Number of maximal matchings in the n-cocktail party graph.
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1
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1, 2, 14, 92, 844, 9304, 121288, 1822736, 31030928, 590248736, 12406395616, 285558273472, 7143371664064, 192972180052352, 5598713198048384, 173627942889668864, 5731684010612723968, 200669613102747214336, 7426773564495661485568, 289713958515451427511296
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OFFSET
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1,2
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COMMENTS
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A maximal matching in the n-cocktail party graph is either a perfect matching or a matching with a single unmatched pair. - Andrew Howroyd, Dec 30 2017
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LINKS
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Eric Weisstein's World of Mathematics, Matching
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FORMULA
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MATHEMATICA
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Table[(-1)^(n + 1) (n HypergeometricPFQ[{1/2, 1 - n}, {}, 2] - HypergeometricPFQ[{1/2, -n}, {}, 2]), {n, 20}]
Table[-I (-1)^n (n HypergeometricU[1/2, n + 1/2, -1/2] - HypergeometricU[1/2, n + 3/2, -1/2])/Sqrt[2], {n, 20}]
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PROG
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b(n)={if(n<1, n==0, sum(k=0, n, (-1)^(n-k)*binomial(n, k)*(2*k)!/(2^k*k!)))}
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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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