A255358 Product_{k=0..n} (k^3)!.

1, 1, 40320, 439039216240867959122165760000000

Offset: 0

Author

Vaclav Kotesovec, Feb 21 2015

Keywords

• nonn

Comments

The next term a(4) has 122 digits.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..6

Crossrefs

Cf. A000178, A255322, A255359, A255360.

Cf. A002109, A051675, A255321, A255323, A255344.

Cf. A000142, A255268, A255269, A255511.

Programs

Mathematica

Table[Product[(k^3)!, {k, 0, n}], {n, 0, 6}]
Table[Product[j^(n - Ceiling[j^(1/3)] + 1), {j, 1, n^3}], {n, 0, 6}] (* Vaclav Kotesovec, Apr 25 2024 *)

Formula

a(n) ~ c * n^(29/40 + 3*n/2 + 3*n^2/4 + 3*n^3/2 + 3*n^4/4) * (2*Pi)^(n/2) / exp(n*(n+2)*(12 - 6*n + 7*n^2)/16), where c = A255511 = 4.113740552015338123052453340090368136...

a(n) = Product_{j=1..n^3} j^(n - ceiling(j^(1/3)) + 1). - Vaclav Kotesovec, Apr 25 2024