A323546 a(n) = Product_{k=0..n} (k^8 + (n-k)^8).

0, 1, 131072, 2843192875329, 94689598336441253888, 30456484467910986480712890625, 24450543078081443740165325452474318848, 74458223912158060479139869222818674648092178561, 545831702006800417886454373052629612732034857946832699392

Offset: 0

Author

Vaclav Kotesovec, Jan 17 2019

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..71

Crossrefs

Cf. A323538, A323540, A323541, A323542, A323543, A323544, A323545, A320345.

Cf. 2*A000542 (with sum instead of product).

Programs

Mathematica

Table[Product[k^8+(n-k)^8, {k, 0, n}], {n, 0, 10}]

PARI

m=8; vector(10, n, n--; prod(k=0,n, k^m + (n-k)^m)) \\ G. C. Greubel, Jan 18 2019

Sage

m=8; [product(k^m +(n-k)^m for k in (0..n)) for n in (0..10)] # G. C. Greubel, Jan 18 2019

Formula

a(n) ~ exp(((2*sqrt(2+sqrt(2)) - 1/2 - sqrt(2))*Pi - 8)*n) * n^(8*n+8).