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
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
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Dec 30 2017
EXTENSIONS
a(9)-a(20) from Andrew Howroyd, Dec 30 2017
STATUS
approved