OFFSET
1,5
COMMENTS
Except for n=2, the number of edges in a maximum matching is floor(n/2). - Andrew Howroyd, Apr 15 2018
LINKS
Eric Weisstein's World of Mathematics, Maximal Independent Edge Set
Eric Weisstein's World of Mathematics, Path Complement Graph
FORMULA
a(n) = Sum_{k=0..floor(n/2)} (-1)^k*binomial(n-k,k)*(2*(ceiling(n/2)-k)-1)!! for n > 2. - Andrew Howroyd, Apr 15 2018
a(n) = 2^-floor(n/2)*n!*hypergeometric1f1(-floor(n/2), -n, -2)/(floor(n/2))! for n > 2. - Eric W. Weisstein, Apr 16 2018
MATHEMATICA
Join[{1, 1}, Table[(2^-Floor[n/2] n! Hypergeometric1F1[-Floor[n/2], -n, -2])/Floor[n/2]!, {n, 3, 30}]]
PROG
(PARI)
b(n)=(2*n)!/(2^n*n!);
a(n)=if(n==2, 1, sum(k=0, n\2, (-1)^k*binomial(n-k, k)*b((n+1)\2-k))); \\ Andrew Howroyd, Apr 15 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Apr 12 2018
EXTENSIONS
a(17)-a(30) from Andrew Howroyd, Apr 15 2018
STATUS
approved