%I #18 Jun 10 2024 23:35:09
%S 1,2,66,16104,16506600,51599631600,401290334953200,
%T 6744887949893385600,221023233230056352726400,
%U 13051421922234827628493920000,1305155243645404997677020493920000,210197862299579765685879504586803840000,52304164669591331834914454764848159918720000
%N Product_{k=0..n} (k^5 + 1).
%H Erhan Gürela, Ali Ulas Özgür Kisisel, <a href="http://dx.doi.org/10.1016/j.jnt.2009.07.014">A note on the products (1^mu + 1)(2^mu + 1)···(n^mu + 1)</a>, Journal of Number Theory, Volume 130, Issue 1, January 2010, Pages 187-191.
%F 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... .
%t Table[Product[k^5 + 1, {k, 0, n}], {n, 0, 15}]
%o (PARI) a(n) = prod(k=1, n, 1+k^5); \\ _Michel Marcus_, Jan 25 2016
%Y Cf. A101686, A255433, A255434, A144664.
%K nonn,easy
%O 0,2
%A _Vaclav Kotesovec_, Feb 23 2015