A384166 a(n) = Product_{k=0..n-1} (3*n+4*k).

1, 3, 60, 1989, 92160, 5486535, 399072960, 34298042625, 3400783626240, 382128386114475, 47986411423104000, 6659996213472126525, 1012334387351519232000, 167253493686752981883375, 29842935065036371998720000, 5719198821953333723419037625, 1171620424982972483984424960000

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Formula

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

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

a(n) = (3/7) * 4^n * n! * binomial(7*n/4,n) for n > 0.

a(n) ~ 7^((7*n-2)/4) * n^n / (3^((3*n-2)/4) * exp(n)). - Amiram Eldar, Dec 08 2025

Mathematica

a[n_] := Product[(3*n+4*k), {k, 0, n-1}]; Table[a[n], {n, 0, 15}] (* Vincenzo Librandi, May 22 2025 *)
a[n_] := (3/7) * 4^n * n! * Binomial[7*n/4, n]; a[0] = 1; Array[a, 18, 0] (* Amiram Eldar, Dec 08 2025 *)

Prog

(PARI) a(n) = prod(k=0, n-1, 3*n+4*k);
(SageMath)
def a(n): return 4^n*rising_factorial(3*n/4, n)
(Python)
from math import prod
def A384166(n): return prod(3*n+i for i in range(0, n<<2, 4)) # Chai Wah Wu, May 21 2025
(Magma) [1] cat  [&*[(3*n + 4*k): k in [0..n-1]]: n in [1..16]]; // Vincenzo Librandi, May 22 2025

Crossrefs

Cf. A384164, A384165.

Cf. A303487.

Sequence in context: A219870 A326283 A259268 * A268964 A361536 A081854

Adjacent sequences: A384163 A384164 A384165 * A384167 A384168 A384169

Keyword

nonn,easy

Author

Seiichi Manyama, May 21 2025

Status

approved