A277352 a(n) = Product_{k=1..n} (2*k^2+1).

1, 3, 27, 513, 16929, 863379, 63026667, 6239640033, 804913564257, 131200910973891, 26371383105752091, 6408246094697758113, 1851983121367652094657, 627822278143634060088723, 246734155310448185614868139, 111277104045012131712305530689

Offset: 0

Author

Vaclav Kotesovec, Oct 10 2016

Keywords

• nonn

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.

Crossrefs

Cf. A101686, A277347, A277353, A277354.

Programs

Mathematica

Table[Product[2*k^2+1, {k, 1, n}], {n, 0, 15}]

PARI

a(n)=prod(k=1,n,2*k^2+1) \\ Charles R Greathouse IV, Mar 16 2023

Formula

a(n) ~ 2^(n+3/2) * n^(2*n+1) * sinh(Pi/sqrt(2)) / exp(2*n).