A330716 n-th Gosper hyperfactorial of n.

1, 1, 16, 1952152956156672

Offset

0,3

Comments

Gosper's m-th hyperfactorial of n is the product 1^(1^m)*2^(2^m)*3^(3^m)*...*n^(n^m).

The 0th hyperfactorial is the factorial function.

References

R. W. Gosper, "Fac Fun" (ca. 1979).

Links

Table of n, a(n) for n=0..3.

R. W. Gosper, Gosper's facfun document

Example

n=3: a(3) = 1^(1^3)*2^(2^3)*3^(3^3) = 2^8 * 3^27.
a(4) has 198 decimal digits and a(5) has 2927 digits.

Mathematica

nmax:=3; Table[Product[i^(i^n), {i, 1, n}], {n, 0, nmax}] (* Stefano Spezia, Dec 29 2019 *)

Crossrefs

Cf. A000142, A002109, A051675, A255321, A255323, A255344 (0th through 5th Gosper hyperfactorials, respectively).

Sequence in context: A291908 A059933 A002488 * A341690 A341689 A243776

Adjacent sequences: A330713 A330714 A330715 * A330717 A330718 A330719

Keyword

nonn,easy

Author

Greg Huber, Dec 27 2019

Status

approved