A384241 a(n) = Product_{k=0..n-1} (3*n-4*k).

1, 3, 12, 45, 0, -3465, -60480, -626535, 0, 204417675, 6227020800, 104928949125, 0, -77849405258625, -3379030566912000, -78792721832199375, 0, 104312208642352585875, 5875458349746585600000, 174954117301479619228125, 0, -362526128354588965187045625, -25100240092118201519308800000

Offset

0,2

Links

Table of n, a(n) for n=0..22.

Formula

a(n) = 4^n * FallingFactorial(3*n/4,n).

a(n) = n! * [x^n] (1 + 4*x)^(3*n/4).

a(n) = 3 * (-1)^(n-1) * A383996(n) for n > 0.

a(4*n) = 0 for n > 0.

Prog

(PARI) a(n) = prod(k=0, n-1, 3*n-4*k);
(SageMath)
def a(n): return 4^n*falling_factorial(3*n/4, n)

Crossrefs

Cf. A064352, A343445.

Cf. A383996, A384166.

Sequence in context: A005656 A339066 A260146 * A229936 A258626 A380047

Adjacent sequences: A384238 A384239 A384240 * A384242 A384243 A384244

Keyword

sign,easy

Author

Seiichi Manyama, May 22 2025

Status

approved