A255434 Product_{k=0..n} (k^4+1).

1, 2, 34, 2788, 716516, 448539016, 581755103752, 1397375759212304, 5725048485492809488, 37567768161803815860256, 375715249386199962418420256, 5501222681512739849730509388352, 114078854746529686263861573186255424, 3258320249270380899068414253345827420288

Offset

0,2

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.

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

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 *)

Prog

(PARI) a(n) = prod(k=1, n, 1+k^4); \\ Michel Marcus, Jan 25 2016

Crossrefs

Cf. A002523, A101686, A255433, A255435, A144663.

Sequence in context: A207865 A216082 A165938 * A206501 A183414 A002782

Adjacent sequences: A255431 A255432 A255433 * A255435 A255436 A255437

Keyword

nonn,easy

Author

Vaclav Kotesovec, Feb 23 2015

Status

approved