cp's OEIS Frontend

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

%I A054479 #32 Mar 06 2023 22:05:11
%S A054479 1,0,6,120,6300,514080,62785800,10676746080,2413521910800,
%T A054479 700039083744000,253445583029839200,112033456760809584000,
%U A054479 59382041886244720843200,37175286835046004765120000,27139206193305890195912400000,22852066417535931447551359680000
%N A054479 Number of sets of cycle graphs of 2n nodes where the 2-colored edges alternate colors.
%C A054479 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
%C A054479 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
%H A054479 Vincenzo Librandi, <a href="/A054479/b054479.txt">Table of n, a(n) for n = 0..200</a>
%F A054479 If b(2n)=a(n) then e.g.f. of b is 1/(sqrt(exp(x^2)*(1-x^2))).
%F A054479 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
%F A054479 a(n) ~ 2^(2*n+1) * n^(2*n) / exp(2*n+1/2). - _Vaclav Kotesovec_, Mar 29 2014
%p A054479 b:= proc(n) option remember; `if`(n=0, 1, add(
%p A054479       b(n-2*j)*binomial(n-1, 2*j-1)*(2*j-1)!, j=2..n/2))
%p A054479     end:
%p A054479 a:= n-> b(2*n):
%p A054479 seq(a(n), n=0..15);  # _Alois P. Heinz_, Mar 06 2023
%t A054479 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_ *)
%o A054479 (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
%Y A054479 Cf. A001147, A001818, A053871, A006712.
%K A054479 nonn
%O A054479 0,3
%A A054479 _Christian G. Bower_, Mar 29 2000