A384257 a(n) = Product_{k=0..n-1} (n+3*k+2).

1, 3, 28, 440, 9720, 276640, 9634240, 396809280, 18866848000, 1016990374400, 61283225203200, 4082333102848000, 297880548623257600, 23628360309345792000, 2024347339040266240000, 186294495108985303040000, 18327479444105919639552000, 1919453757320555804508160000

Offset

0,2

Links

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

Formula

a(n) = 3^n * RisingFactorial((n+2)/3,n).

a(n) = n! * [x^n] 1/(1 - 3*x)^((n+2)/3).

Prog

(PARI) a(n) = prod(k=0, n-1, n+3*k+2);
(SageMath)
def a(n): return 3^n*rising_factorial((n+2)/3, n)

Crossrefs

Cf. A303486, A384256.

Sequence in context: A219532 A376034 A319369 * A340789 A210854 A060545

Adjacent sequences: A384254 A384255 A384256 * A384258 A384259 A384260

Keyword

nonn,easy

Author

Seiichi Manyama, May 23 2025

Status

approved