A376523 a(n) = Product_{k=0..n} (k^3 + n - k).

0, 1, 32, 2187, 286720, 64796875, 23279477760, 12506434235113, 9582123576983552, 10084099499408154825, 14139206937856000000000, 25756714724499975610869475, 59683270195198565091221962752, 172781591936242461223503558613507, 615312169743368293769528795463680000

Offset: 0

Author

Vaclav Kotesovec, Sep 26 2024

Keywords

• nonn

Crossrefs

Cf. A323541, A374881, A374886, A376524.

Programs

Maple

A376523 := proc(n)
    mul(k^3+n-k,k=0..n) ;
end proc:
seq(A376523(n),n=0..20) ; # R. J. Mathar, Sep 27 2024

Mathematica

Table[Product[k^3+n-k, {k, 0, n}], {n, 0, 16}]

Formula

a(n) ~ exp(2*Pi*n^(1/3)/sqrt(3) - 3*n) * n^(3*n+2) * (1 - 2*Pi/(3^(3/2)*n^(1/3)) + 2*Pi^2/(27*n^(2/3)) + (27/40 - 4*Pi^3/(243*sqrt(3)))/n).