A255269 a(n) = Product_{k=1..n} k!^k.

1, 4, 864, 286654464, 7132880358604800000, 993710590042385551668019200000000000, 82086865668400428790437436119503664712777728000000000000000000

Offset

1,2

Links

Table of n, a(n) for n=1..7.

Eric Weisstein's World of Mathematics, Hyperfactorial

Eric Weisstein's World of Mathematics, Superfactorial

Formula

a(n) = A255268(n) / A055462(n-1).

a(n) ~ sqrt(A) * exp((3 - 45*n^2 - 32*n^3 - 9*Zeta(3)/Pi^2)/72) * n^((8*n^3 + 18*n^2 + 10*n + 1)/24) * (2*Pi)^(n*(n+1)/4), where A = A074962 = 1.28242712910062263687534256886979... is the Glaisher-Kinkelin constant and Zeta(3) = A002117 = 1.2020569031595942853997... .

Mathematica

Table[Product[k!^k, {k, 1, n}], {n, 1, 10}]
FoldList[Times, Table[(k!)^k, {k, 10}]] (* Harvey P. Dale, Aug 16 2021 *)

Crossrefs

Cf. A000178, A002109, A036740, A055462, A255268.

Sequence in context: A332184 A221232 A272167 * A113896 A159706 A349077

Adjacent sequences: A255266 A255267 A255268 * A255270 A255271 A255272

Keyword

nonn

Author

Vaclav Kotesovec, Feb 20 2015

Status

approved