OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..150
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.
Chuan Ze Niu, (1^3+1)(2^3+1)...(n^3+1) is not a cube, arXiv:1612.08158 [math.NT], 2016.
FORMULA
a(n) ~ 2*sqrt(2*Pi) * cosh(sqrt(3)*Pi/2) * n^(3*n + 3/2) / exp(3*n).
a(n) = 2*A158621(n). - Vaclav Kotesovec, Jul 11 2015
MATHEMATICA
Table[Product[k^3 + 1, {k, 0, n}], {n, 0, 20}]
FullSimplify[Table[(Cosh[Sqrt[3]*Pi/2] * Gamma[2+n] * Gamma[1/2 - I*Sqrt[3]/2 + n] * Gamma[1/2 + I*Sqrt[3]/2 + n])/Pi, {n, 0, 20}]]
FoldList[Times, Range[0, 20]^3+1] (* Harvey P. Dale, Jul 07 2017 *)
PROG
(PARI) a(n) = prod(k=1, n, 1+k^3); \\ Michel Marcus, Jan 25 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vaclav Kotesovec, Feb 23 2015
STATUS
approved