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A171881
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Square array, read by antidiagonals, where T(n,k)=n^^k for n>=0, k>=1.
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1
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0, 1, 1, 2, 1, 1, 3, 4, 1, 1, 4, 27, 16, 1, 1, 5, 256, 19683, 256, 1, 1, 6, 3125, 4294967296, 7625597484987, 65536, 1, 1, 7, 46656, 298023223876953125, 340282366920938463463374607431768211456
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OFFSET
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0,4
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COMMENTS
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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)).
More terms on Munafo website.
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LINKS
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EXAMPLE
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Array begins:
0,1,1,1,1,1,...
1,1,1,1,1,1,...
2,4,16,256,65536,...
3,27,19683,...
4,256,4294967296,...
5,3125,...
6,46656,...
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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