A323544 -id:A323544 - cp's OEIS frontend

A323662 a(n) = Product_{k=0..n} (k^13 + (n-k)^13).

0, 1, 134217728, 170623376651175378921, 187556828900191806607614608932864, 17233921359224498311699145473539829254150390625, 3651108402083969086976039852657366429953837378356052425179136

Offset: 0

Vaclav Kotesovec, Jan 23 2019

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..48

Cf. A323540, A323541, A323542, A323543, A323544, A323545, A323546, A320345, A323659, A323660, A323661.

Table[Product[k^13+(n-k)^13, {k, 0, n}], {n, 0, 10}]

a(n) ~ exp((2*Pi*sqrt((2699 - 1920*cos(2*Pi/13) + 4184*cos(3*Pi/13) - 4512*sin(Pi/26) + 4752*sin(3*Pi/26) - 2944*sin(5*Pi/26))/13) / 13 - 12)*n) * n^(13*n+13).

A323751 a(n) = Product_{k=0..n} (k^n + (n-k)^n).

Original entry on oeis.org

2, 1, 32, 59049, 14101250048, 775913238525390625, 13410804447068120796679372800, 112244673425189306235795780017831813874289, 545831702006800417886454373052629612732034857946832699392

Offset: 0

Seiichi Manyama, Jan 26 2019

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..27

Cf. A323540, A323541, A323542, A323543, A323544, A323545, A323546.

Cf. A323575, A323588.

[(&*[k^n +(n-k)^n: k in [0..n]]): n in [0..10]]; // G. C. Greubel, Feb 08 2019

Table[Product[k^n+(n-k)^n, {k,0,n}], {n,0,10}] (* G. C. Greubel, Feb 08 2019 *)

PARI
```
{a(n) = prod(k=0, n, k^n+(n-k)^n)}
```

[product(k^n +(n-k)^n for k in (0..n)) for n in (0..10)] # G. C. Greubel, Feb 08 2019

a(n) = n^n * A323588(n). - Vaclav Kotesovec, Feb 08 2019

cp's OEIS Frontend

A323662 a(n) = Product_{k=0..n} (k^13 + (n-k)^13).

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