cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A376523 #8 Sep 27 2024 05:20:52
%S A376523 0,1,32,2187,286720,64796875,23279477760,12506434235113,
%T A376523 9582123576983552,10084099499408154825,14139206937856000000000,
%U A376523 25756714724499975610869475,59683270195198565091221962752,172781591936242461223503558613507,615312169743368293769528795463680000
%N A376523 a(n) = Product_{k=0..n} (k^3 + n - k).
%F A376523 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).
%p A376523 A376523 := proc(n)
%p A376523     mul(k^3+n-k,k=0..n) ;
%p A376523 end proc:
%p A376523 seq(A376523(n),n=0..20) ; # _R. J. Mathar_, Sep 27 2024
%t A376523 Table[Product[k^3+n-k, {k, 0, n}], {n, 0, 16}]
%Y A376523 Cf. A323541, A374881, A374886, A376524.
%K A376523 nonn
%O A376523 0,3
%A A376523 _Vaclav Kotesovec_, Sep 26 2024