A165422 a(1) = 1, a(2) = 4, a(n) = product of the previous terms for n >= 3.

1, 4, 4, 16, 256, 65536, 4294967296, 18446744073709551616, 340282366920938463463374607431768211456, 115792089237316195423570985008687907853269984665640564039457584007913129639936

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..13

Formula

a(1) = 1, a(2) = 4, a(n) = Product_{i=1..n-1} a(i), n >= 3.

a(1) = 1, a(2) = 4, a(n) = A000302(2^(n-3)) = A001146(n-2) = 2^(2^(n-2)), n >= 3.

a(1) = 1, a(2) = 4, a(3) = 4, a(n) = (a(n-1))^2, n >= 4.

From Amiram Eldar, Nov 30 2025: (Start)

Sum_{n>=1} 1/a(n) = 3/4 + A007404.

Product_{n>=1} (1 + 1/a(n)) = 10/3.

Product_{n>=2} (1 - 1/a(n)) = (3/2) * A215016. (End)

Mathematica

a[1]:= 1; a[2]:= 4; a[n_] := Product[a[j], {j, 1, n-1}]; Table[a[n], {n, 1, 12}] (* G. C. Greubel, Oct 19 2018 *)
Join[{1, 4}, NestList[#^2&, 4, 10]] (* Harvey P. Dale, Aug 26 2019 *)

Prog

(PARI) {a(n) = if(n==1, 1, if(n==2, 4, prod(j=1, n-1, a(j))))};
for(n=1, 10, print1(a(n), ", ")) \\ G. C. Greubel, Oct 19 2018

Crossrefs

Essentially the same as A001146.

Cf. A000302, A007404, A215016.

Sequence in context: A019062 A019013 A340425 * A051460 A191972 A101407

Adjacent sequences: A165419 A165420 A165421 * A165423 A165424 A165425

Keyword

nonn

Author

Jaroslav Krizek, Sep 17 2009

Status

approved