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%I #18 Apr 17 2024 08:00:52
%S 0,2,6,40,210,1260,7392,44616,270270,1653080,10161580,62783448,
%T 389398464,2423339800,15123958200,94621687200,593266344930,
%U 3726769133340,23450149615200,147778547947800,932531767467300,5891770693620240,37265696746444920,235945424360833200
%N a(n) = binomial(2*n,n) * Fibonacci(n).
%F a(n) = 2 * A119693(n).
%F Sum_{n>=0} a(n)/8^n = sqrt(2/5). - _Amiram Eldar_, May 04 2023
%F G.f.: -(2*sqrt(-16*x^2-4*x+1)-16*x-2)/(sqrt(10)*sqrt(-16*x^2-4*x+1)*sqrt(4*sqrt(-16*x^2-4*x+1)+8*x+6)). - _Vladimir Kruchinin_, Apr 17 2024
%p seq(binomial(2*n, n)*combinat[fibonacci](n), n=0..27);
%t Table[Binomial[2n,n]Fibonacci[n],{n,0,20}] (* _Harvey P. Dale_, Feb 29 2012 *)
%Y Cf. A000045, A000984, A119693.
%K easy,nonn,changed
%O 0,2
%A _Zerinvary Lajos_, Jun 09 2006
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