A252730 a(n) = P_n(n) with P_0(z) = z+1 and P_n(z) = z + P_{n-1}(z)*(P_{n-1}(z)-z) for n>1.

1, 3, 17, 871, 4870849, 483209576974811, 36956045653220845240164417232897, 8498748758632331927648392184620600167779995785955324343380396911247

Offset: 0

Author

Alois P. Heinz, Dec 20 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10
• A. V. Aho and N. J. A. Sloane, Some doubly exponential sequences, Fibonacci Quarterly, Vol. 11, No. 4 (1973), pp. 429-437.
• A. V. Aho and N. J. A. Sloane, Some doubly exponential sequences, Fibonacci Quarterly, Vol. 11, No. 4 (1973), pp. 429-437 (original plus references that F.Q. forgot to include - see last page!)

Crossrefs

Main diagonal of A177888.

Programs

Maple

p:= proc(n) option remember;
      z-> z+ `if`(n=0, 1, p(n-1)(z)*(p(n-1)(z)-z))
    end:
a:= n-> p(n)(n):
seq(a(n), n=0..8);

Mathematica

p[n_] := p[n] = Function[z, z + If[n == 0, 1, p[n-1][z]*(p[n-1][z] - z)]];
a[n_] := p[n][n];
Table[a[n], {n, 0, 8}] (* Jean-François Alcover, Jun 12 2018, from Maple *)