A274306 a(n) = Product_{k=1..n} (4*k^4+1).

1, 5, 325, 105625, 108265625, 270772328125, 1403954521328125, 13484983177356640625, 220951449360988556640625, 5798870788479144669033203125, 231960630409954265905997158203125, 13584774319958971582784723570166015625

Offset

0,2

Links

Table of n, a(n) for n=0..11.

Erhan Gürel, On the Occurrence of Perfect Squares Among Values of Certain Polynomial Products, The American Mathematical Monthly 123.6 (2016): 597-599.

Formula

a(n) ~ (1 + cosh(Pi)) * 2^(2*n + 2) * n^(4*n + 2) / exp(4*n). - Vaclav Kotesovec, Oct 10 2016

Mathematica

Table[Product[4*k^4+1, {k, 1, n}], {n, 0, 15}] (* Vaclav Kotesovec, Oct 10 2016 *)

Prog

(PARI) a(n) = prod(k=1, n, 4*k^4+1); \\ Michel Marcus, Oct 10 2016

Crossrefs

For squares in this sequence see A274307.

Cf. A255434.

Sequence in context: A212041 A251696 A366329 * A053516 A085523 A292687

Adjacent sequences: A274303 A274304 A274305 * A274307 A274308 A274309

Keyword

nonn

Author

N. J. A. Sloane, Jun 20 2016

Status

approved