A323544 - OEIS

A323544

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

%I #15 Sep 08 2022 08:46:23

%S 0,1,8192,2245338225,1144394036019200,2577023355527587890625,

%T 13410804447068120796679372800,172661401915668867785003701060950625,

%U 4548909593429214367033270472265433088000000,234845240509381890690238640158397433600579682850625

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

%H Seiichi Manyama, <a href="/A323544/b323544.txt">Table of n, a(n) for n = 0..90</a>

%F a(n) ~ exp(((15 - 4*sqrt(3))*Pi/6 - 6)*n) * n^(6*n+6).

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

%o (Magma) [(&*[(k^6 + (n-k)^6): k in [0..n]]): n in [0..10]]; // _Vincenzo Librandi_, Jan 18 2019

%o (PARI) m=6; vector(10, n, n--; prod(k=0,n, k^m + (n-k)^m)) \\ _G. C. Greubel_, Jan 18 2019

%o (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

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

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

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Jan 17 2019