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

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, 65536, 1, 1, 1, 6, 3125, 13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096

Offset

0,8

Comments

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

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

More terms on Munafo website.

Links

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

R. Munafo, Hyper4 Iterated Exponential Function

Index entries for sequences related to tetration

Example

Array begins:
1,0,1,0,1,0,1,...
1,1,1,1,1,1,1,...
1,2,4,16,65536,...
1,3,27,7625597484987,...
1,4,256,...
1,5,3125,...
1,6,46656,...

Crossrefs

Cf. A171881, A321312 (by downwards diagonals).

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

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

Main diagonal A004231 (Ackermann's sequence).

Sequence in context: A003992 A337161 A246118 * A214075 A322267 A286933

Adjacent sequences: A171879 A171880 A171881 * A171883 A171884 A171885

Keyword

nonn,tabl

Author

Robert Munafo, Jan 21 2010

Status

approved