A323544 a(n) = Product_{k=0..n} (k^6 + (n-k)^6).

0, 1, 8192, 2245338225, 1144394036019200, 2577023355527587890625, 13410804447068120796679372800, 172661401915668867785003701060950625, 4548909593429214367033270472265433088000000, 234845240509381890690238640158397433600579682850625

Offset: 0

Author

Vaclav Kotesovec, Jan 17 2019

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..90

Crossrefs

Cf. A323534, A323540, A323541, A323542, A323543, A323545, A323546.

Cf. 2*A000540 and A259109 (with sum instead of product).

Programs

Magma

[(&*[(k^6 + (n-k)^6): k in [0..n]]): n in [0..10]]; // Vincenzo Librandi, Jan 18 2019

Mathematica

Table[Product[k^6+(n-k)^6, {k, 0, n}], {n, 0, 10}]

PARI

m=6; vector(10, n, n--; prod(k=0,n, k^m + (n-k)^m)) \\ G. C. Greubel, Jan 18 2019

Sage

m=6; [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(((15 - 4*sqrt(3))*Pi/6 - 6)*n) * n^(6*n+6).