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A177888 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. 9
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Antidiagonals n = 0..13, flattened

A. V. Aho and N. J. A. Sloane, Some doubly exponential sequences, Fib. Quart., 11 (1973), 429-437.

EXAMPLE

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,        ...

MAPLE

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);

MATHEMATICA

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-Fran├žois Alcover, Dec 13 2013, translated from Maple *)

CROSSREFS

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).

Rows n=0-2 give: A000027(k+1), A005408, A056220(k+1).

Main diagonal gives A252730.

Coefficients of P_n(z) give: A177701.

Sequence in context: A210552 A193376 A185095 * A073020 A090349 A157379

Adjacent sequences:  A177885 A177886 A177887 * A177889 A177890 A177891

KEYWORD

nonn,tabl

AUTHOR

Alois P. Heinz, Dec 14 2010

STATUS

approved

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Last modified December 16 15:01 EST 2018. Contains 318171 sequences. (Running on oeis4.)