A323588 a(n) = Product_{k=1..n} (k^n + (n-k)^n).
1, 1, 8, 2187, 55083008, 248292236328125, 287440081598682287308800, 136294854579772162759923622710449623, 32534104705262209051040075603284216686012438413312, 5686543339012978225006873713961872387810223003912610672810622880089
Offset: 0
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 0..27
Programs
-
Magma
[1] cat [(&*[k^n +(n-k)^n: k in [1..n]]): n in [1..10]]; // G. C. Greubel, Feb 08 2019
-
Mathematica
Table[Product[k^n+(n-k)^n, {k, 1, n}], {n, 0, 10}] -
PARI
vector(10, n, n--; prod(k=1,n, k^n+(n-k)^n)) \\ G. C. Greubel, Feb 08 2019
-
Sage
[product(k^n +(n-k)^n for k in (1..n)) for n in (0..10)] # G. C. Greubel, Feb 08 2019
Formula
a(n) ~ c * 2^(n^2) * n^(n^2) / exp(n^2), where
c = 1.7567468186007109703792640049745420817202851050652253469714... if n is even,
c = 1.8080216158688347442204158454365469233524049331246880759722... if n is odd.