A323715 a(n) = Product_{k=0..n} (2^k + 3^k).

2, 10, 130, 4550, 441350, 121371250, 96247401250, 222812733893750, 1518914406953693750, 30674476448429845281250, 1842707823686526095580531250, 330204028465507043697553297343750, 176836474792332245660656600199579843750

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. A000079, A000244, A007689, A323716, A369680.

Programs

Magma

[(&*[3^j+2^j: j in [0..n]]): n in [0..20]]; // G. C. Greubel, Aug 30 2023

Mathematica

Table[Product[2^k+3^k, {k, 0, n}], {n, 0, 12}]
Table[2^(n*(n+1)/2)*QPochhammer[-1, 3/2, n+1], {n, 0, 12}]

PARI

a(n) = prod(k=0, n, 2^k+3^k); \\ Michel Marcus, Jan 25 2019

SageMath

[product(3^j+2^j 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 = QPochhammer[-1, 2/3] = 10.934481779448897533...