A323542 a(n) = Product_{k=0..n} (k^4 + (n-k)^4).

0, 1, 512, 1896129, 14101250048, 242755875390625, 7888809923487203328, 452522453429009743939201, 42521926771106843499966758912, 6212193882217859346149080691430849, 1350441156698962215630405632000000000000, 421551664651621436548685508587919503984205889

Offset: 0

Author

Vaclav Kotesovec, Jan 17 2019

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..125

Crossrefs

Cf. A272247, A323497, A323540, A323541, A323543, A323544, A323545, A323546.

Cf. 2*A000538 and A259108 (with sum instead of product).

Programs

Magma

[(&*[(k^4 + (n-k)^4): k in [0..n]]): n in [0..15]]; // Vincenzo Librandi, Jan 18 2019

Mathematica

Table[Product[k^4+(n-k)^4, {k, 0, n}], {n, 0, 15}]

PARI

m=4; vector(15, n, n--; prod(k=0,n, k^m + (n-k)^m)) \\ G. C. Greubel, Jan 18 2019

Sage

m=4; [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((Pi*(sqrt(2) - 1/2) - 4)*n) * n^(4*n + 4).