A323541 a(n) = Product_{k=0..n} (k^3 + (n-k)^3).

0, 1, 128, 59049, 51380224, 80869140625, 207351578198016, 811509810302822449, 4603095542875667038208, 36344623587588604291790241, 386644580358400000000000000000, 5395532942025804980378907333844441, 96578621213529440721046520779140759552

Offset: 0

Author

Vaclav Kotesovec, Jan 17 2019

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..158

Crossrefs

Cf. A272246, A323496, A323540, A323542, A323543, A323544, A323545, A323546.

Cf. 2*A000537 and A163102 (with sum instead of product).

Programs

Magma

m:=3; [(&*[k^m + (n-k)^m: k in [0..n]]): n in [0..15]]; // G. C. Greubel, Jan 18 2019

Mathematica

Table[Product[k^3+(n-k)^3, {k, 0, n}], {n, 0, 15}]

PARI

m=3; vector(15, n, n--; prod(k=0,n, k^m + (n-k)^m)) \\ G. C. Greubel, Jan 18 2019

Sage

m=3; [product(k^m +(n-k)^m for k in (0..n)) for n in (0..15)] # G. C. Greubel, Jan 18 2019

Formula

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