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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

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..14.

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).

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