A306907 a(n) = Product_{i=0..n, j=0..n, k=0..n} (i*j*k + 1).

1, 2, 60750, 193002701276968128000000, 5076574217867350877310882935055477754989937924247841796875000000000000

Offset: 0

Author

Vaclav Kotesovec, Mar 25 2019

Keywords

• nonn

Comments

Next term is too long to be included.

Crossrefs

Cf. A306760, A307106.

Programs

Mathematica

Table[Product[i*j*k+1,{i,0,n},{j,0,n},{k,0,n}],{n,0,5}]

Formula

a(n) = (n!)^(3*n^2) * Product_{i=1..n, j=1..n, k=1..n} (1 + 1/(i*j*k)).

a(n) ~ exp(3*n^2*log(Gamma(n+1)) + (gamma + PolyGamma(0, n+1))^3 - c), where gamma is the Euler-Mascheroni constant A001620 and c = A307106 = Sum_{k>=2} (-1)^k * Zeta(k)^3 / k = 1.836921908595663783265640880112170343162564662453544904457...

a(n) ~ (2*Pi)^(3*n^2/2) * exp(-3*n^3 + n/4 + (log(n))^3 + 3*gamma*(log(n))^2 + gamma^3 - c) * n^(3*(n^3 + n^2/2 + gamma^2)).