A344057 a(n) = (2*n)! / CatalanNumber(n - 1) for n >= 1 and a(0) = 1.

1, 2, 24, 360, 8064, 259200, 11404800, 660441600, 48771072000, 4477184409600, 500391198720000, 66920738734080000, 10554356508917760000, 1938789402181632000000, 410402940653807861760000, 99180710658003566592000000, 27141314475238493257728000000

Offset: 0

Author

Peter Luschny, May 12 2021

Keywords

• nonn

Crossrefs

Cf. A000108, A010050.

Programs

Mathematica

a[n_] := (2 n)! / CatalanNumber[n - 1]; a[0] := 1; Table[a[n], {n, 0, 16}]

Python

from math import factorial
def A344057(n):
    return 1 if n == 0 else 2*n**2*(2*n-1)*factorial(n-1)**2 # Chai Wah Wu, May 12 2021

Formula

a(n) = A010050(n)/A000108(n-1) for n>=1. - Michel Marcus, May 12 2021

a(n) = 2*n*(2*n-1)*(n-1)!*n! = 2*n^2*(2*n-1)*((n-1)!)^2 for n > 0. a(n) = a(n-1)*n^2*(2*n - 1)/(2*n - 3) for n > 1. - Chai Wah Wu, May 12 2021