OFFSET
0,6
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..350
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 677
FORMULA
D-finite with recurrence: a(1)=0, a(2)=0, a(4)=0, a(3)=0, a(5)=120, a(6)=2880, (n+2)*a(n+2) = (6*n^2 + 8*n - 8)*a(n+1) + (40 + 44*n = 4*n^2 - 8*n^3)*a(n).
a(n) = 2*Pi^(-1/2)*4^(n-3)*Gamma(n-5/2)*n*(n-4) for n>3. - Mark van Hoeij, Oct 30 2011
a(n) = n!*A002057(n-5). - R. J. Mathar, Oct 18 2013
From G. C. Greubel, May 28 2022: (Start)
G.f.: 4!*x*(d/dx)( x^5 * Hypergeometric2F0([2, 5/2], [], 4*x) ).
E.g.f.: (x/2)*(1 - 4*x + 2*x^2 - (1-2*x)*sqrt(1-4*x)). (End)
MAPLE
spec := [S, {C=Union(B, Z), B=Prod(C, C), S=Prod(B, B, Z)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
MATHEMATICA
Table[If[n<5, 0, 2*n*(n-2)!*(n-4)*CatalanNumber[n-3]], {n, 0, 30}] (* G. C. Greubel, May 28 2022 *)
PROG
(SageMath)
def A052721(n):
if (n<5): return 0
else: return 2*n*factorial(n-2)*(n-4)*catalan_number(n-3)
[A052721(n) for n in (0..30)] # G. C. Greubel, May 28 2022
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
STATUS
approved