|
%I #5 Mar 30 2012 18:37:33
%S 1,1,3,15,93,655,5025,40995,350665,3116083,28588541,269632839,
%T 2606374433,25766661303,260133432037,2679336234403,28138284922321,
%U 301224023801747,3286962740398689,36567211855460123,414883492490364865,4802747139352783619,56754591674540964917
%N G.f. satisfies: A(x) = Sum_{n>=0} x^n * (2*A(x)^n - 1)^n.
%F G.f. satisfies: A(x) = Sum_{n>=0} 2^n*x^n * A(x)^(n^2)/(1 + x*A(x)^n)^(n+1).
%e G.f.: A(x) = 1 + x + 3*x^2 + 15*x^3 + 93*x^4 + 655*x^5 + 5025*x^6 +...
%e where the g.f. satisfies following series identity:
%e A(x) = 1 + (2*A(x)-1)*x + (2*A(x)^2-1)^2*x^2 + (2*A(x)^3-1)^3*x^3 + (2*A(x)^4-1)^4*x^4 +...
%e A(x) = 1/(1+x) + 2*x*A(x)/(1+x*A(x))^2 + 2^2*x^2*A(x)^4/(1+x*A(x)^2)^3 + 2^3*x^3*A(x)^9/(1+x*A(x)^3)^4 + 2^4*x^4*A(x)^16/(1+x*A(x)^4)^5 +...
%o (PARI) {a(n)=local(A=1+x);for(i=1,n,A=sum(k=0, n, (2*A^k-1+x*O(x^n))^k*x^k));polcoeff(A, n)}
%o (PARI) {a(n)=local(A=1+x);for(i=1,n,A=sum(k=0, n, 2^k*A^(k^2)*x^k/(1+A^k*x+x*O(x^n))^(k+1) ));polcoeff(A, n)}
%Y Cf. A203000.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Dec 27 2011
|
