[go: up one dir, main page]

login
A323575
a(n) = Product_{k=1..n} (k^k + (n-k)^k).
9
1, 1, 8, 405, 229376, 1827109375, 257063481999360, 755170478103207873707, 54143353027014803410072371200, 107483342384971486221625795626923693445, 6647872853044955947850033397760000000000000000000, 14166017880429890423491783342799863539312599105433301729629445
OFFSET
0,3
LINKS
FORMULA
a(n) ~ c * n^(n*(n+1)/2) * 2^(n^2/2) / exp(n^2/2), where c = A303641 = 2.473655256632129487637893694272428036362097123254579382787777122619864038942...
MATHEMATICA
Table[Product[k^k+(n-k)^k, {k, 1, n}], {n, 0, 12}]
PROG
(PARI) vector(12, n, n--; prod(k=1, n, k^k+(n-k)^k)) \\ G. C. Greubel, Feb 08 2019
(Magma) [1] cat [(&*[k^k +(n-k)^k: k in [1..n]]): n in [1..12]]; // 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
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Jan 18 2019
STATUS
approved