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A171882 Square array, read by antidiagonals, where T(n,k)=n^^k for n>=0, k>=0. 2


%S 1,1,0,1,1,1,1,2,1,0,1,3,4,1,1,1,4,27,16,1,0,1,5,256,7625597484987,

%T 65536,1,1,1,6,3125,

%U 13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096

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

%C n^^k defined the right-associative way: n^^2=n^n, n^^3=n^(n^n), n^^4=n^(n^(n^n)), etc.

%C n^^0=1 by convention, so that n^^(k+1) = n^(n^^k) for all k>=0.

%C More terms on Munafo website.

%H R. Munafo, <a href="http://mrob.com/pub/math/hyper4.html">Hyper4 Iterated Exponential Function</a>

%H <a href="/index/Te#tetration">Index entries for sequences related to tetration</a>

%e Array 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,...

%Y Cf. A171881, A321312 (by downwards diagonals).

%Y Rows n=0 to 4: A059841, A000012, A014221, A014222, A114561.

%Y Columns k=0 to 3: A000012, A001477, A000312, A002488.

%Y Main diagonal A004231 (Ackermann's sequence).

%K nonn,tabl

%O 0,8

%A _Robert Munafo_, Jan 21 2010

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Last modified April 19 20:37 EDT 2021. Contains 343117 sequences. (Running on oeis4.)