A255435 Product_{k=0..n} (k^5 + 1).

1, 2, 66, 16104, 16506600, 51599631600, 401290334953200, 6744887949893385600, 221023233230056352726400, 13051421922234827628493920000, 1305155243645404997677020493920000, 210197862299579765685879504586803840000, 52304164669591331834914454764848159918720000

Offset

0,2

Links

Table of n, a(n) for n=0..12.

Erhan Gürela, Ali Ulas Özgür Kisisel, A note on the products (1^mu + 1)(2^mu + 1)···(n^mu + 1), Journal of Number Theory, Volume 130, Issue 1, January 2010, Pages 187-191.

Formula

a(n) ~ c * n^(5*n+5/2) / exp(5*n), where c = 4 * sqrt(2) * Pi^(5/2) / abs(Gamma(3/4 + sqrt(5)/4 + i*sqrt(5/8 + sqrt(5)/8)) * Gamma(3/4 - sqrt(5)/4 + i*sqrt(5/8 - sqrt(5)/8)))^2 = 205.260576646551853296... .

Mathematica

Table[Product[k^5 + 1, {k, 0, n}], {n, 0, 15}]

Prog

(PARI) a(n) = prod(k=1, n, 1+k^5); \\ Michel Marcus, Jan 25 2016

Crossrefs

Cf. A101686, A255433, A255434, A144664.

Sequence in context: A361884 A261784 A350730 * A335546 A139822 A119552

Adjacent sequences: A255432 A255433 A255434 * A255436 A255437 A255438

Keyword

nonn,easy

Author

Vaclav Kotesovec, Feb 23 2015

Status

approved