A323575 a(n) = Product_{k=1..n} (k^k + (n-k)^k).

1, 1, 8, 405, 229376, 1827109375, 257063481999360, 755170478103207873707, 54143353027014803410072371200, 107483342384971486221625795626923693445, 6647872853044955947850033397760000000000000000000, 14166017880429890423491783342799863539312599105433301729629445

Offset: 0

Author

Vaclav Kotesovec, Jan 18 2019

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..36

Crossrefs

Cf. A323540-A323546, A323588, A323589, A303641.

Programs

Magma

[1] cat [(&*[k^k +(n-k)^k: k in [1..n]]): n in [1..12]]; // G. C. Greubel, Feb 08 2019

Mathematica

Table[Product[k^k+(n-k)^k, {k, 1, n}], {n, 0, 12}]

PARI

vector(12, n, n--; prod(k=1,n, k^k+(n-k)^k)) \\ G. C. Greubel, Feb 08 2019

Sage

[product(k^k +(n-k)^k for k in (1..n)) for n in (0..12)] # G. C. Greubel, Feb 08 2019

Formula

a(n) ~ c * n^(n*(n+1)/2) * 2^(n^2/2) / exp(n^2/2), where c = A303641 = 2.473655256632129487637893694272428036362097123254579382787777122619864038942...