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A323541 a(n) = Product_{k=0..n} (k^3 + (n-k)^3). 14

%I

%S 0,1,128,59049,51380224,80869140625,207351578198016,

%T 811509810302822449,4603095542875667038208,36344623587588604291790241,

%U 386644580358400000000000000000,5395532942025804980378907333844441,96578621213529440721046520779140759552

%N a(n) = Product_{k=0..n} (k^3 + (n-k)^3).

%H Seiichi Manyama, <a href="/A323541/b323541.txt">Table of n, a(n) for n = 0..158</a>

%F a(n) ~ exp(2*(Pi/(3*sqrt(3))-1)*n) * n^(3*n + 3).

%t Table[Product[k^3+(n-k)^3, {k, 0, n}], {n, 0, 15}]

%o (PARI) m=3; vector(15, n, n--; prod(k=0,n, k^m + (n-k)^m)) \\ _G. C. Greubel_, Jan 18 2019

%o (MAGMA) m:=3; [(&*[k^m + (n-k)^m: k in [0..n]]): n in [0..15]]; // _G. C. Greubel_, Jan 18 2019

%o (Sage) m=3; [product(k^m +(n-k)^m for k in (0..n)) for n in (0..15)] # _G. C. Greubel_, Jan 18 2019

%Y Cf. A272246, A323496, A323540, A323542, A323543, A323544, A323545, A323546.

%Y Cf. 2*A000537 and A163102 (with sum instead of product).

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Jan 17 2019

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Last modified April 19 18:20 EDT 2019. Contains 322283 sequences. (Running on oeis4.)