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 A297474 Number of maximal matchings in the n-cocktail party graph. 0
 1, 2, 14, 92, 844, 9304, 121288, 1822736, 31030928, 590248736, 12406395616, 285558273472, 7143371664064, 192972180052352, 5598713198048384, 173627942889668864, 5731684010612723968, 200669613102747214336, 7426773564495661485568, 289713958515451427511296 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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 LINKS Eric Weisstein's World of Mathematics, Cocktail Party Graph Eric Weisstein's World of Mathematics, Matching Eric Weisstein's World of Mathematics, Maximal Independent Edge Set FORMULA a(n) = A053871(n) + n*A053871(n-1). - Andrew Howroyd, Dec 30 2017 MATHEMATICA 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}] PROG (PARI) \\ here b(n) is A053871. b(n)={if(n<1, n==0, sum(k=0, n, (-1)^(n-k)*binomial(n, k)*(2*k)!/(2^k*k!)))} a(n)=b(n) + n*b(n-1); \\ Andrew Howroyd, Dec 30 2017 CROSSREFS Cf. A053871. Sequence in context: A288470 A341395 A072148 * A270063 A033169 A090410 Adjacent sequences:  A297471 A297472 A297473 * A297475 A297476 A297477 KEYWORD nonn AUTHOR Eric W. Weisstein, Dec 30 2017 EXTENSIONS a(9)-a(20) from Andrew Howroyd, Dec 30 2017 STATUS approved

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Last modified April 13 21:24 EDT 2021. Contains 342941 sequences. (Running on oeis4.)