A323543 a(n) = Product_{k=0..n} (k^5 + (n-k)^5).

0, 1, 2048, 64304361, 3995393327104, 775913238525390625, 320224500476333990608896, 273342392644434762426370643281, 429621172463958849019228299940855808, 1175198860360296464427314161342724729270241, 5278148679274118560000000000000000000000000000000

Offset: 0

Author

Vaclav Kotesovec, Jan 17 2019

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..104

Crossrefs

Cf. A272248, A323533, A323540, A323541, A323542, A323544, A323545, A323546.

Cf. 2*A000539 (with sum instead of product).

Programs

Magma

[(&*[(k^5 + (n-k)^5): k in [0..n]]): n in [0..12]]; // Vincenzo Librandi, Jan 18 2019

Mathematica

Table[Product[k^5+(n-k)^5, {k, 0, n}], {n, 0, 12}]

PARI

m=5; vector(12, n, n--; prod(k=0,n, k^m +(n-k)^m)) \\ G. C. Greubel, Jan 18 2019

Sage

m=5; [product(k^m +(n-k)^m for k in (0..n)) for n in (0..12)] # G. C. Greubel, Jan 18 2019

Formula

a(n) ~ exp((2*Pi*sqrt(5 - 2/sqrt(5))/5 - 4)*n) * n^(5*n+5).