A255359 a(n) = Product_{k=0..n} (k^4)!.

1, 1, 20922789888000

Offset: 0

Author

Vaclav Kotesovec, Feb 21 2015

Keywords

• nonn

Comments

The next term a(3) has 135 digits.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..4

Crossrefs

Cf. A000178, A255322, A255358, A255360.

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

Cf. A000142, A255268, A255269, A255438.

Programs

Mathematica

Table[Product[(k^4)!, {k, 0, n}], {n, 0, 5}]
Table[Product[j^(n - Ceiling[j^(1/4)] + 1), {j, 1, n^4}], {n, 0, 5}] (* Vaclav Kotesovec, Apr 25 2024 *)

Formula

a(n) ~ c * n^(1 + 28*n/15 + 4*n^3/3 + 2*n^4 + 4*n^5/5) * (2*Pi)^(n/2) / exp(19*n/9 + n^4/2 + 9*n^5/25), where c = A255438 = 6.644987918706354049483118... .

a(n) = Product_{j=1..n^4} j^(n - ceiling(j^(1/4)) + 1). - Vaclav Kotesovec, Apr 25 2024