This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A321312 #20 Feb 16 2025 08:33:57 %S A321312 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 A321312 256,5,1 %N A321312 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 A321312 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PowerTower.html">Power Tower</a> %H A321312 Wikipedia, <a href="https://en.wikipedia.org/wiki/Knuth%27s_up-arrow_notation">Knuth's up-arrow notation</a> %H A321312 Wikipedia, <a href="https://en.wikipedia.org/wiki/Tetration">Tetration</a> %H A321312 <a href="/index/Te#tetration">Index entries for sequences related to tetration</a> %e A321312 Square array A(n,k) begins: %e A321312 1, 0, 1, 0, 1, 0, 1, ... %e A321312 1, 1, 1, 1, 1, 1, 1, ... %e A321312 1, 2, 4, 16, 65536, ... %e A321312 1, 3, 27, 7625597484987, ... %e A321312 1, 4, 256, ... %e A321312 1, 5, 3125, ... %e A321312 1, 6, 46656, ... %e A321312 1, 7, 823543, ... %e A321312 ... %p A321312 A:= (n, k)-> `if`(k=0, 1, n^A(n, k-1)): %p A321312 seq(seq(A(n, d-n), n=0..d), d=0..6); %Y A321312 Columns k=0-3 give: A000012, A001477, A000312, A002488. %Y A321312 Rows n=0-4 give: A059841, A000012, A014221, A014222(k+1), A114561(k+1). %Y A321312 Main diagonal gives A004231 (Ackermann's sequence). %Y A321312 Cf. A027747, A171882 (by upwards diagonals). %K A321312 nonn,tabl %O A321312 0,9 %A A321312 _Alois P. Heinz_, Nov 03 2018