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

%I A171881 #9 Oct 29 2021 05:04:03
%S A171881 0,1,1,2,1,1,3,4,1,1,4,27,16,1,1,5,256,19683,256,1,1,6,3125,
%T A171881 4294967296,7625597484987,65536,1,1,7,46656,298023223876953125,
%U A171881 340282366920938463463374607431768211456
%N A171881 Square array, read by antidiagonals, where T(n,k)=n^^k for n>=0, k>=1.
%C A171881 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)).
%C A171881 More terms on Munafo website.
%H A171881 Robert Munafo, <a href="http://mrob.com/pub/math/hyper4.html">Hyper4 Iterated Exponential Function</a>.
%e A171881 Array begins:
%e A171881   0,1,1,1,1,1,...
%e A171881   1,1,1,1,1,1,...
%e A171881   2,4,16,256,65536,...
%e A171881   3,27,19683,...
%e A171881   4,256,4294967296,...
%e A171881   5,3125,...
%e A171881   6,46656,...
%t A171881 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 *)
%Y A171881 Cf. A171882.
%K A171881 nonn,tabl
%O A171881 0,4
%A A171881 _Robert Munafo_, Jan 21 2010