%I #19 Apr 05 2021 20:56:50
%S 1,0,1,1,1,1,0,1,2,1,1,1,4,3,1,0,1,16,27,4,1,1,1,65536,7625597484987,
%T 256,5,1
%N A(n,k) = n^^k is the k-th tetration of n; square array A(n,k), n>=0, k>=0, read by antidiagonals.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PowerTower.html">Power Tower</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Knuth%27s_up-arrow_notation">Knuth's up-arrow notation</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Tetration">Tetration</a>
%H <a href="/index/Te#tetration">Index entries for sequences related to tetration</a>
%e Square array A(n,k) begins:
%e 1, 0, 1, 0, 1, 0, 1, ...
%e 1, 1, 1, 1, 1, 1, 1, ...
%e 1, 2, 4, 16, 65536, ...
%e 1, 3, 27, 7625597484987, ...
%e 1, 4, 256, ...
%e 1, 5, 3125, ...
%e 1, 6, 46656, ...
%e 1, 7, 823543, ...
%e ...
%p A:= (n, k)-> `if`(k=0, 1, n^A(n, k-1)):
%p seq(seq(A(n, d-n), n=0..d), d=0..6);
%Y Columns k=0-3 give: A000012, A001477, A000312, A002488.
%Y Rows n=0-4 give: A059841, A000012, A014221, A014222(k+1), A114561(k+1).
%Y Main diagonal gives A004231 (Ackermann's sequence).
%Y Cf. A027747, A171882 (by upwards diagonals).
%K nonn,tabl
%O 0,9
%A _Alois P. Heinz_, Nov 03 2018