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A274306 a(n) = Product_{k=1..n} (4*k^4+1). 2
1, 5, 325, 105625, 108265625, 270772328125, 1403954521328125, 13484983177356640625, 220951449360988556640625, 5798870788479144669033203125, 231960630409954265905997158203125, 13584774319958971582784723570166015625 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

Erhan G├╝rel, 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: A304212 A212041 A251696 * A053516 A085523 A292687

Adjacent sequences:  A274303 A274304 A274305 * A274307 A274308 A274309

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jun 20 2016

STATUS

approved

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Last modified April 19 22:22 EDT 2019. Contains 322291 sequences. (Running on oeis4.)