A368064 a(n) = Product_{i=1..n, j=1..n} (i^2 + 4*i*j + j^2).

1, 6, 24336, 870746557824, 1311726482483997806493696, 256433546267136937832915286844640487014400, 15678550451426175377500759401206644047210595564950427820202393600

Offset

0,2

Links

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

Formula

a(n) ~ 2^((3+sqrt(3))*n*(n+1) + (sqrt(3)-1)/6) * 3^(3*n*(n+1) + 13/24) * n^(2*n^2 - 7/6) / (Gamma(1/3)^(1/2) * Gamma(1/4)^(1/3) * Pi^(7/12) * (1 + sqrt(3))^((6*n*(n+1) + 1)/sqrt(3) - 1/2) * exp(3*n^2)).

Mathematica

Table[Product[i^2 + 4*i*j + j^2, {i, 1, n}, {j, 1, n}], {n, 0, 7}]

Crossrefs

Cf. A367543, A324403, A367542, A079478^2, A368067, A368065, A368066.

Sequence in context: A376824 A283887 A241650 * A337990 A143780 A225716

Adjacent sequences: A368061 A368062 A368063 * A368065 A368066 A368067

Keyword

nonn

Author

Vaclav Kotesovec, Dec 10 2023

Status

approved