A323716 a(n) = Product_{k=0..n} (3^k + 1).

2, 8, 80, 2240, 183680, 44817920, 32717081600, 71584974540800, 469740602936729600, 9246374028206585446400, 545998386365598870609920000, 96722522147893108730806108160000, 51402410615320609490117059732766720000

Offset: 0

Author

Vaclav Kotesovec, Jan 25 2019

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..64

Crossrefs

Cf. A028361, A034472, A132323, A323715.

Programs

Magma

[(&*[3^j+1: j in [0..n]]): n in [0..20]]; // G. C. Greubel, Aug 30 2023

Mathematica

Table[Product[3^k+1, {k, 0, n}], {n, 0, 12}]
Table[QPochhammer[-1, 3, n+1], {n, 0, 12}]

PARI

a(n) = prod(k=0, n, 3^k+1); \\ Michel Marcus, Jan 25 2019

SageMath

[product(3^j+1 for j in range(n+1)) for n in range(21)] # G. C. Greubel, Aug 30 2023

Formula

a(n) ~ c * 3^(n*(n+1)/2), where c = A132323 = QPochhammer[-1, 1/3] = 3.12986803713402307587769821345767...