A274306 - OEIS

%I #16 Oct 10 2016 05:14:30

%S 1,5,325,105625,108265625,270772328125,1403954521328125,

%T 13484983177356640625,220951449360988556640625,

%U 5798870788479144669033203125,231960630409954265905997158203125,13584774319958971582784723570166015625

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

%H Erhan Gürel, <a href="http://www.jstor.org/stable/10.4169/amer.math.monthly.123.6.597">On the Occurrence of Perfect Squares Among Values of Certain Polynomial Products</a>, The American Mathematical Monthly 123.6 (2016): 597-599.

%F a(n) ~ (1 + cosh(Pi)) * 2^(2*n + 2) * n^(4*n + 2) / exp(4*n). - _Vaclav Kotesovec_, Oct 10 2016

%t Table[Product[4*k^4+1, {k,1,n}], {n, 0, 15}] (* _Vaclav Kotesovec_, Oct 10 2016 *)

%o (PARI) a(n) = prod(k=1, n, 4*k^4+1); \\ _Michel Marcus_, Oct 10 2016

%Y For squares in this sequence see A274307.

%Y Cf. A255434.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Jun 20 2016