A054479 Number of sets of cycle graphs of 2n nodes where the 2-colored edges alternate colors.

1, 0, 6, 120, 6300, 514080, 62785800, 10676746080, 2413521910800, 700039083744000, 253445583029839200, 112033456760809584000, 59382041886244720843200, 37175286835046004765120000, 27139206193305890195912400000, 22852066417535931447551359680000

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

Cf. A001147, A001818, A053871, A006712.

Sequence in context: A331640 A012641 A012795 * A012475 A053777 A023199

Adjacent sequences: A054476 A054477 A054478 * A054480 A054481 A054482

Keyword

nonn

Author

Christian G. Bower, Mar 29 2000

Status

approved