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A323589 a(n) = Product_{k=1..n-1} (k^k + (n-k)^(n-k)).

%I A323589 #12 Sep 08 2022 08:46:23
%S A323589 1,1,2,25,6272,63473089,35671256150400,1706937496190389809801,
%T A323589 7511133178157708431911079116800,
%U A323589 4755809816953036991699151550498501702425129,394143276257895110158515904775794405720952934400000000000
%N A323589 a(n) = Product_{k=1..n-1} (k^k + (n-k)^(n-k)).
%H A323589 G. C. Greubel, <a href="/A323589/b323589.txt">Table of n, a(n) for n = 0..31</a>
%F A323589 a(n) ~ n^(3*n^2/4 - n) * 2^(n^2/4 + 7/6) / exp(3*n^2/8) if n is even.
%F A323589 a(n) ~ n^(3*n^2/4 - n + 1/4) * 2^(n^2/4 - 1/12) / exp(3*n^2/8 - 1/4) if n is odd.
%t A323589 Table[Product[k^k+(n-k)^(n-k), {k, 1, n-1}], {n, 0, 12}]
%o A323589 (PARI) vector(12, n, n--; prod(k=1,n-1, k^k+(n-k)^(n-k))) \\ _G. C. Greubel_, Feb 08 2019
%o A323589 (Magma) [1,1] cat [(&*[k^k + (n-k)^(n-k): k in [1..n-1]]): n in [2..12]]; // _G. C. Greubel_, Feb 08 2019
%o A323589 (Sage) [product(k^k + (n-k)^(n-k) for k in (1..n-1)) for n in (0..12)] # _G. C. Greubel_, Feb 08 2019
%Y A323589 Cf. A323575, A323588.
%K A323589 nonn
%O A323589 0,3
%A A323589 _Vaclav Kotesovec_, Jan 18 2019