OFFSET
0,3
COMMENTS
Also number of permutations in the symmetric group S_2n in which cycle lengths are even and greater than 2, cf. A130915. - Vladeta Jovovic, Aug 25 2007
a(n) is also the number of ordered pairs of disjoint perfect matchings in the complete graph on 2n vertices. The sequence A006712 is the number of ordered triples of perfect matchings. - Matt Larson, Jul 23 2016
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
FORMULA
If b(2n)=a(n) then e.g.f. of b is 1/(sqrt(exp(x^2)*(1-x^2))).
a(n) = 4^n*(n-1)*gamma(n+1/2)^2*hypergeom([2-n],[3/2-n],-1/2)/(Pi*(n-1/2)). - Mark van Hoeij, May 13 2013
a(n) ~ 2^(2*n+1) * n^(2*n) / exp(2*n+1/2). - Vaclav Kotesovec, Mar 29 2014
MAPLE
b:= proc(n) option remember; `if`(n=0, 1, add(
b(n-2*j)*binomial(n-1, 2*j-1)*(2*j-1)!, j=2..n/2))
end:
a:= n-> b(2*n):
seq(a(n), n=0..15); # Alois P. Heinz, Mar 06 2023
MATHEMATICA
Table[(n-1)*(2*n)!^2 * HypergeometricPFQ[{2-n}, {3/2-n}, -1/2] / (4^n*(n-1/2)*(n!)^2), {n, 0, 20}] (* Vaclav Kotesovec, Mar 29 2014 after Mark van Hoeij *)
PROG
(PARI) x='x+O('x^66); v=Vec(serlaplace(1/(sqrt(exp(x^2)*(1-x^2))))); vector(#v\2, n, v[2*n-1]) \\ Joerg Arndt, May 13 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Christian G. Bower, Mar 29 2000
STATUS
approved