A255434 Product_{k=0..n} (k^4+1).
1, 2, 34, 2788, 716516, 448539016, 581755103752, 1397375759212304, 5725048485492809488, 37567768161803815860256, 375715249386199962418420256, 5501222681512739849730509388352, 114078854746529686263861573186255424, 3258320249270380899068414253345827420288
Offset: 0
Links
- Harvey P. Dale, Table of n, a(n) for n = 0..144
- 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^4 + 1, {k, 0, n}], {n, 0, 15}] FoldList[Times,Range[0,15]^4+1] (* Harvey P. Dale, Nov 01 2022 *) -
PARI
a(n) = prod(k=1, n, 1+k^4); \\ Michel Marcus, Jan 25 2016
Formula
a(n) ~ 2 * (cosh(sqrt(2)*Pi) - cos(sqrt(2)*Pi)) * n^(4*n+2) / exp(4*n).
a(n) ~ A258870 * (n!)^4. - Vaclav Kotesovec, May 16 2022