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

0,3

Links

Table of n, a(n) for n=0..17.

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

Prog

(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)
(SageMath)
def a(n): return rising_factorial(2*n-1, n)

Crossrefs

Cf. A064352, A352601.

Cf. A090816, A117671.

Sequence in context: A342502 A334886 A027399 * A266910 A296681 A231260

Adjacent sequences: A384258 A384259 A384260 * A384262 A384263 A384264

Keyword

nonn,easy

Author

Seiichi Manyama, May 23 2025

Status

approved