A367943 a(n) = Product_{i=1..n, j=1..n} (i^2 + 4*j^2).

1, 5, 13600, 294372000000, 252880261890048000000000, 27099784799070466617992871936000000000000, 882065676199020188908312950703217787436793856000000000000000000

Offset

0,2

Links

Table of n, a(n) for n=0..6.

Formula

a(n) ~ c * n^(2*n^2 - 1/2) * 5^(n*(n+1)) * 2^(-n) * exp(n*(n+1)*(2*Pi - 3*arctan(2))/2 - 3*n^2) , where c = 0.4523180383519335764034720087114905921141637339852374451758854101884791581...

Mathematica

Table[Product[i^2+4*j^2, {i, 1, n}, {j, 1, n}], {n, 0, 8}]

Crossrefs

Cf. A324403, A367941, A367942, A367944.

Cf. A367542, A367543.

Sequence in context: A242772 A368067 A364691 * A089989 A219011 A297482

Adjacent sequences: A367940 A367941 A367942 * A367944 A367945 A367946

Keyword

nonn

Author

Vaclav Kotesovec, Dec 05 2023

Status

approved