A171881 Square array, read by antidiagonals, where T(n,k)=n^^k for n>=0, k>=1.

0, 1, 1, 2, 1, 1, 3, 4, 1, 1, 4, 27, 16, 1, 1, 5, 256, 19683, 256, 1, 1, 6, 3125, 4294967296, 7625597484987, 65536, 1, 1, 7, 46656, 298023223876953125, 340282366920938463463374607431768211456

Offset

0,4

Comments

n^^k is defined the left-associative way: n^^2=n^n, n^^3=(n^n)^n=n^(n^2), n^^4=((n^n)^n)^n=n^(n^3), and in general n^^k=n^(n^(k-1)).

More terms on Munafo website.

Links

Table of n, a(n) for n=0..31.

Robert Munafo, Hyper4 Iterated Exponential Function.

Example

Array begins:
  0,1,1,1,1,1,...
  1,1,1,1,1,1,...
  2,4,16,256,65536,...
  3,27,19683,...
  4,256,4294967296,...
  5,3125,...
  6,46656,...

Mathematica

T[n_, k_] := If[n == 0, Boole[k != 0], n^(n^k)]; Table[T[k, n - k], {n, 0, 7}, {k, n, 0, -1}] // Flatten (* Amiram Eldar, Oct 29 2021 *)

Crossrefs

Cf. A171882.

Sequence in context: A104495 A093541 A336187 * A321877 A320251 A210341

Adjacent sequences: A171878 A171879 A171880 * A171882 A171883 A171884

Keyword

nonn,tabl

Author

Robert Munafo, Jan 21 2010

Status

approved