A384261 a(n) = Product_{k=0..n-1} (2*n+k-1).
1, 1, 12, 210, 5040, 154440, 5765760, 253955520, 12893126400, 741354768000, 47621141568000, 3379847863392000, 262662462526464000, 22183557976419840000, 2023140487449489408000, 198155371076302768128000, 20744817468539834621952000, 2311708772421640603275264000
Offset: 0
Programs
-
PARI
a(n) = prod(k=0, n-1, 2*n+k-1);
-
Python
from sympy import rf def a(n): return rf(2*n-1, n)
-
Sage
def a(n): return rising_factorial(2*n-1, n)
Formula
a(n) = RisingFactorial(2*n-1,n).
a(n) = n! * [x^n] 1/(1 - x)^(2*n-1).
a(n) = n! * binomial(3*n-2,n).
D-finite with recurrence 2*(-2*n+3)*a(n) +3*(3*n-2)*(3*n-4)*a(n-1)=0. - R. J. Mathar, May 26 2025