A252730 - OEIS

%I #14 Jan 09 2025 09:59:00

%S 1,3,17,871,4870849,483209576974811,36956045653220845240164417232897,

%T 8498748758632331927648392184620600167779995785955324343380396911247

%N 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.

%H Alois P. Heinz, <a href="/A252730/b252730.txt">Table of n, a(n) for n = 0..10</a>

%H A. V. Aho and N. J. A. Sloane, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/11-4/aho-a.pdf">Some doubly exponential sequences</a>, Fibonacci Quarterly, Vol. 11, No. 4 (1973), pp. 429-437.

%H A. V. Aho and N. J. A. Sloane, <a href="/A000058/a000058.pdf">Some doubly exponential sequences</a>, Fibonacci Quarterly, Vol. 11, No. 4 (1973), pp. 429-437 (original plus references that F.Q. forgot to include - see last page!)

%p p:= proc(n) option remember;

%p       z-> z+ `if`(n=0, 1, p(n-1)(z)*(p(n-1)(z)-z))

%p     end:

%p a:= n-> p(n)(n):

%p seq(a(n), n=0..8);

%t p[n_] := p[n] = Function[z, z + If[n == 0, 1, p[n-1][z]*(p[n-1][z] - z)]];

%t a[n_] := p[n][n];

%t Table[a[n], {n, 0, 8}] (* _Jean-François Alcover_, Jun 12 2018, from Maple *)

%Y Main diagonal of A177888.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Dec 20 2014