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%I #9 Jun 28 2014 07:54:12
%S 1,1,4,26,236,2756,39376,665464,12986416,287394416,7112021696,
%T 194607175136,5834321568064,190181750900416,6697115871398656,
%U 253362903806266496,10248299242094541056,441359565949128552704,20163160035504969573376,973917774772339989408256
%N E.g.f.: exp( Sum_{n>=1} Fibonacci(2*n)*x^n/n ).
%H Vaclav Kotesovec, <a href="/A244451/b244451.txt">Table of n, a(n) for n = 0..380</a>
%F E.g.f.: ( (1 - x/Phi^2) / (1 - Phi^2*x) )^(sqrt(5)/5) where Phi = (sqrt(5)+1)/2.
%F E.g.f.: exp( Integral 1/(1-3*x+x^2) dx ).
%F a(n) ~ n! * 5^(1/(2*sqrt(5))) * n^(1/sqrt(5)-1) * ((1+sqrt(5))/2)^(2*n-2/sqrt(5)) / GAMMA(1/sqrt(5)). - _Vaclav Kotesovec_, Jun 28 2014
%e E.g.f.: A(x) = 1 + x + 4*x^2/2! + 26*x^3/3! + 236*x^4/4! + 2756*x^5/5! +...
%e where
%e log(A(x)) = x + 3*x^2/2 + 8*x^3/3 + 21*x^4/4 + 55*x^5/5 + 144*x^6/6 + 377*x^7/7 + 987*x^8/8 +...+ A000045(2*n)*x^n/n +...
%o (PARI) {a(n)=n!*polcoeff(exp(intformal(1/(1-3*x+x^2 +x*O(x^n)))), n)}
%o for(n=0, 30, print1(a(n), ", "))
%Y Cf. A244430, A000045.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jun 28 2014
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