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 A177377 G.f. satisfies: A(x) = Sum_{n>=0} x^n*A(x)^Fibonacci(n). 0

%I #2 Mar 30 2012 18:37:21

%S 1,1,2,4,9,22,58,164,497,1621,5749,22572,100753,528778,3376927,

%T 26917694,270793597,3438163325,54872573755,1096972396453,

%U 27415834320206,855886182233279,33367897950658859,1624569696575576124

%N G.f. satisfies: A(x) = Sum_{n>=0} x^n*A(x)^Fibonacci(n).

%e G.f.: A(x) = 1 + x + 2*x^2 + 4*x^3 + 9*x^4 + 22*x^5 + 58*x^6 +...

%e A(x) = 1 + x*A(x) + x^2*A(x) + x^3*A(x)^2 + x^4*A(x)^3 + x^5*A(x)^5 + x^6*A(x)^8 + x^7*A(x)^13 + x^8*A(x)^21 + x^9*A(x)^34 + x^10*A(x)^55 +...

%o (PARI) {a(n)=local(A=1+x);for(i=1,n,A=sum(k=0,n,x^k*(A+x*O(x^n))^fibonacci(k)));polcoeff(A,n)}

%Y Cf. A000045.

%K nonn

%O 0,3

%A _Paul D. Hanna_, May 07 2010

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