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Largest coefficient in expansion of P(0)=x, P(n+1)=P(n)*[1+P(n)].
3

%I #3 Apr 30 2014 01:30:31

%S 1,1,2,10,302,391232,912140731560,6870302396056798235043564,

%T 552249828443015013351729477795257932661645918815144

%N Largest coefficient in expansion of P(0)=x, P(n+1)=P(n)*[1+P(n)].

%C It would be nice to have a formula for the 2^(n-1)th coefficient.

%C The exponent of x in P(n) with a(n) as coefficient is {1,1,2,5,9,19,37,74,147,294,587,1175,...}.

%o (PARI) P(n)=if(n<1,x,P(n-1)*(P(n-1)+1))

%o (PARI) a(n)=vecmax(Vec(P(n)))

%Y Cf. A016131.

%K nonn

%O 0,3

%A _Ralf Stephan_, Apr 02 2004