OFFSET
0,2
COMMENTS
Guadalupe proves that a(n) is not square for n > 0. - Charles R Greathouse IV, Mar 16 2023
LINKS
Russelle Guadalupe, Squares of the form Product_{k=1..n} (2k^2+l) with l odd, arXiv:2201.00501 [math.NT], 2022.
FORMULA
a(n) ~ 2^(n+3/2) * n^(2*n+1) * sinh(Pi/sqrt(2)) / exp(2*n).
MATHEMATICA
Table[Product[2*k^2+1, {k, 1, n}], {n, 0, 15}]
PROG
(PARI) a(n)=prod(k=1, n, 2*k^2+1) \\ Charles R Greathouse IV, Mar 16 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Oct 10 2016
STATUS
approved