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A177888
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P_n(k) with P_0(z) = z+1 and P_n(z) = z + P_(n-1)(z)*(P_(n-1)(z)-z) for n>1; square array P_n(k), n>=0, k>=0, read by antidiagonals.
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9
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1, 2, 1, 3, 3, 1, 4, 5, 7, 1, 5, 7, 17, 43, 1, 6, 9, 31, 257, 1807, 1, 7, 11, 49, 871, 65537, 3263443, 1, 8, 13, 71, 2209, 756031, 4294967297, 10650056950807, 1, 9, 15, 97, 4691, 4870849, 571580604871, 18446744073709551617, 113423713055421844361000443, 1
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OFFSET
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0,2
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LINKS
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EXAMPLE
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Square array P_n(k) begins:
1, 2, 3, 4, 5, 6, 7, 8, ...
1, 3, 5, 7, 9, 11, 13, 15, ...
1, 7, 17, 31, 49, 71, 97, 127, ...
1, 43, 257, 871, 2209, 4691, 8833, 15247, ...
1, 1807, 65537, 756031, 4870849, ...
1, 3263443, 4294967297, ...
1, 10650056950807, ...
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MAPLE
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p:= proc(n) option remember;
z-> z+ `if`(n=0, 1, p(n-1)(z)*(p(n-1)(z)-z))
end:
seq(seq(p(n)(d-n), n=0..d), d=0..8);
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MATHEMATICA
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p[n_] := p[n] = Function[z, z + If [n == 0, 1, p[n-1][z]*(p[n-1][z]-z)] ]; Table [Table[p[n][d-n], {n, 0, d}], {d, 0, 8}] // Flatten (* Jean-François Alcover, Dec 13 2013, translated from Maple *)
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CROSSREFS
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Columns k=0-10 give: A000012, A000058(n+1), A000215, A000289(n+1), A000324(n+1), A001543(n+1), A001544(n+1), A067686, A110360(n+1), A110368(n+1), A110383(n+1).
Coefficients of P_n(z) give: A177701.
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KEYWORD
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AUTHOR
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STATUS
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approved
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