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A323588 a(n) = Product_{k=1..n} (k^n + (n-k)^n). 6

%I #13 Sep 08 2022 08:46:23

%S 1,1,8,2187,55083008,248292236328125,287440081598682287308800,

%T 136294854579772162759923622710449623,

%U 32534104705262209051040075603284216686012438413312,5686543339012978225006873713961872387810223003912610672810622880089

%N a(n) = Product_{k=1..n} (k^n + (n-k)^n).

%H G. C. Greubel, <a href="/A323588/b323588.txt">Table of n, a(n) for n = 0..27</a>

%F a(n) ~ c * 2^(n^2) * n^(n^2) / exp(n^2), where

%F c = 1.7567468186007109703792640049745420817202851050652253469714... if n is even,

%F c = 1.8080216158688347442204158454365469233524049331246880759722... if n is odd.

%t Table[Product[k^n+(n-k)^n, {k, 1, n}], {n, 0, 10}]

%o (PARI) vector(10, n, n--; prod(k=1,n, k^n+(n-k)^n)) \\ _G. C. Greubel_, Feb 08 2019

%o (Magma) [1] cat [(&*[k^n +(n-k)^n: k in [1..n]]): n in [1..10]]; // _G. C. Greubel_, Feb 08 2019

%o (Sage) [product(k^n +(n-k)^n for k in (1..n)) for n in (0..10)] # _G. C. Greubel_, Feb 08 2019

%Y Cf. A323540-A323546, A323575, A323589, A323751.

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Jan 18 2019

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Last modified March 28 14:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)