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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.

%I A252730 #14 Jan 09 2025 09:59:00
%S A252730 1,3,17,871,4870849,483209576974811,36956045653220845240164417232897,
%T A252730 8498748758632331927648392184620600167779995785955324343380396911247
%N 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.
%H A252730 Alois P. Heinz, <a href="/A252730/b252730.txt">Table of n, a(n) for n = 0..10</a>
%H A252730 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 A252730 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 A252730 p:= proc(n) option remember;
%p A252730       z-> z+ `if`(n=0, 1, p(n-1)(z)*(p(n-1)(z)-z))
%p A252730     end:
%p A252730 a:= n-> p(n)(n):
%p A252730 seq(a(n), n=0..8);
%t A252730 p[n_] := p[n] = Function[z, z + If[n == 0, 1, p[n-1][z]*(p[n-1][z] - z)]];
%t A252730 a[n_] := p[n][n];
%t A252730 Table[a[n], {n, 0, 8}] (* _Jean-François Alcover_, Jun 12 2018, from Maple *)
%Y A252730 Main diagonal of A177888.
%K A252730 nonn
%O A252730 0,2
%A A252730 _Alois P. Heinz_, Dec 20 2014