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a(n) = 2 a(n-1)^2 + 1 for n >=2 , where a(0) = 1, a(1) = 1.
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%I #9 May 29 2022 18:00:30

%S 1,1,3,19,723,1045459,2185969041363,9556921299594946409795539,

%T 182669489453303118864862198078197846848343568601043,

%U 66736284754260838751569986258667504511444731209422184665239731909577328659648804587017101288201375699

%N a(n) = 2 a(n-1)^2 + 1 for n >=2 , where a(0) = 1, a(1) = 1.

%C (a(n)) is a strong divisibility sequence.

%F a(n) = p(n,0), where p(n,x) is polynomial defined in A329432.

%t f[x_] := 2 x^2 + 1; u[0, x_] := 1;

%t u[1, x_] := f[x]; u[n_, x_] := f[u[n - 1, x]]

%t Table [u[n, x] /. x -> 0, {n, 0, 10}]

%Y Cf. A329432.

%K nonn

%O 0,3

%A _Clark Kimberling_, Dec 31 2019