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A255269 a(n) = Product_{k=1..n} k!^k. 12
1, 4, 864, 286654464, 7132880358604800000, 993710590042385551668019200000000000, 82086865668400428790437436119503664712777728000000000000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
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
Sequence in context: A332184 A221232 A272167 * A113896 A159706 A349077
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Feb 20 2015
STATUS
approved

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Last modified April 17 08:05 EDT 2024. Contains 371756 sequences. (Running on oeis4.)