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A207835 G.f.: exp( Sum_{n>=1} 5*L(n)*x^n/n ), where L(n) = Fibonacci((n-1)^2) + Fibonacci((n+1)^2).

%I A207835 #13 Mar 30 2012 18:37:37
%S A207835 1,15,200,3525,134355,16781664,6730280105,7679335074975,
%T A207835 23795707614699850,197148338964056588955,4337960355881995023988299,
%U A207835 252594793852565664429620014530,38838042059493582778244565420563025,15744729667082405326504405819215652913325
%N A207835 G.f.: exp( Sum_{n>=1} 5*L(n)*x^n/n ), where L(n) = Fibonacci((n-1)^2) + Fibonacci((n+1)^2).
%C A207835 Given g.f. A(x), note that A(x)^(1/5) is not an integer series.
%C A207835 Compare the definition to the g.f. of the Fibonacci numbers:
%C A207835 1/(1-x-x^2) = exp( Sum_{n>=1} Lucas(n)*x^n/n ), where Lucas(n) = Fibonacci(n-1) + Fibonacci(n+1).
%e A207835 G.f.: A(x) = 1 + 15*x + 200*x^2 + 3525*x^3 + 134355*x^4 + 16781664*x^5 +...
%e A207835 such that, by definition,
%e A207835 log(A(x))/5 = 3*x + 35*x^2/2 + 990*x^3/3 + 75059*x^4/4 + 14931339*x^5/5 + 7778817074*x^6/6 +...+ (Fibonacci((n-1)^2) + Fibonacci((n+1)^2))*x^n/n +...
%o A207835 (PARI) {L(n)=fibonacci((n-1)^2)+fibonacci((n+1)^2)}
%o A207835 {a(n)=polcoeff(exp(sum(m=1,n,5*L(m)*x^m/m)+x*O(x^n)),n)}
%o A207835 for(n=0,21,print1(a(n),", "))
%Y A207835 Cf. A207834, A156216, A166168.
%K A207835 nonn
%O A207835 0,2
%A A207835 _Paul D. Hanna_, Feb 20 2012