A255435 Product_{k=0..n} (k^5 + 1).
1, 2, 66, 16104, 16506600, 51599631600, 401290334953200, 6744887949893385600, 221023233230056352726400, 13051421922234827628493920000, 1305155243645404997677020493920000, 210197862299579765685879504586803840000, 52304164669591331834914454764848159918720000
Offset: 0
Links
- 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.
Programs
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Mathematica
Table[Product[k^5 + 1, {k, 0, n}], {n, 0, 15}] -
PARI
a(n) = prod(k=1, n, 1+k^5); \\ Michel Marcus, Jan 25 2016
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... .