A372116 a(n) = Product_{k=0..n} (n+k)!^k.

1, 2, 3456, 128994508800000, 21048441369734473363614597120000000000, 13080442484467245346116306952031286205761554346416540536012800000000000000000000

Offset

0,2

Comments

The next term has 146 digits.

Links

Table of n, a(n) for n=0..5.

Formula

a(n) ~ 2^(2*n^3/3 + 5*n^2/4 + 2*n/3 + 1/24) * Pi^(n*(n+1)/4) * n^(5*n^3/6 + 5*n^2/4 + 5*n/12) / exp(31*n^3/36 + 7*n^2/8 - 1/24).

For n>=1, a(n) = a(n-1) * A368132(n) * (2*n-1)!^n.

Mathematica

Table[Product[(n + k)!^k, {k, 0, n}], {n, 0, 8}]

Crossrefs

Cf. A055462, A255269, A296591, A367492, A368132.

Sequence in context: A099689 A065671 A094211 * A350418 A114573 A285086

Adjacent sequences: A372113 A372114 A372115 * A372117 A372118 A372119

Keyword

nonn

Author

Vaclav Kotesovec, Apr 19 2024

Status

approved