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A323543 a(n) = Product_{k=0..n} (k^5 + (n-k)^5). 14

%I

%S 0,1,2048,64304361,3995393327104,775913238525390625,

%T 320224500476333990608896,273342392644434762426370643281,

%U 429621172463958849019228299940855808,1175198860360296464427314161342724729270241,5278148679274118560000000000000000000000000000000

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

%H Seiichi Manyama, <a href="/A323543/b323543.txt">Table of n, a(n) for n = 0..104</a>

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

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

%o (MAGMA) [(&*[(k^5 + (n-k)^5): k in [0..n]]): n in [0..12]]; // _Vincenzo Librandi_, Jan 18 2019

%o (PARI) m=5; vector(12, n, n--; prod(k=0,n, k^m +(n-k)^m)) \\ _G. C. Greubel_, Jan 18 2019

%o (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

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

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

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Jan 17 2019

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Last modified March 24 11:49 EDT 2019. Contains 321448 sequences. (Running on oeis4.)