A323589 a(n) = Product_{k=1..n-1} (k^k + (n-k)^(n-k)).
1, 1, 2, 25, 6272, 63473089, 35671256150400, 1706937496190389809801, 7511133178157708431911079116800, 4755809816953036991699151550498501702425129, 394143276257895110158515904775794405720952934400000000000
Offset: 0
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 0..31
Programs
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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
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Mathematica
Table[Product[k^k+(n-k)^(n-k), {k, 1, n-1}], {n, 0, 12}] -
PARI
vector(12, n, n--; prod(k=1,n-1, k^k+(n-k)^(n-k))) \\ G. C. Greubel, Feb 08 2019
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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
Formula
a(n) ~ n^(3*n^2/4 - n) * 2^(n^2/4 + 7/6) / exp(3*n^2/8) if n is even.
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.