%I #24 Jan 15 2020 01:05:53

%S 1,1,16,1952152956156672

%N n-th Gosper hyperfactorial of n.

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

%C The 0th hyperfactorial is the factorial function.

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

%H R. W. Gosper, <a href="/A330716/a330716.pdf">Gosper's facfun document</a>

%e n=3: a(3) = 1^(1^3)*2^(2^3)*3^(3^3) = 2^8 * 3^27.

%e a(4) has 198 decimal digits and a(5) has 2927 digits.

%t nmax:=3; Table[Product[i^(i^n),{i,1,n}],{n,0,nmax}] (* _Stefano Spezia_, Dec 29 2019 *)

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

%K nonn,easy

%O 0,3

%A _Greg Huber_, Dec 27 2019