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a(n) = n*binomial(2*n, n)*Fibonacci(n).
1

%I #12 May 05 2023 01:38:31

%S 0,2,12,120,840,6300,44352,312312,2162160,14877720,101615800,

%T 690617928,4672781568,31503417400,211735414800,1419325308000,

%U 9492261518880,63355075266780,422102693073600,2807792411008200,18650635349346000,123727184566025040,819845328421788240

%N a(n) = n*binomial(2*n, n)*Fibonacci(n).

%H Harvey P. Dale, <a href="/A119701/b119701.txt">Table of n, a(n) for n = 0..1000</a>

%F Sum_{n>=0} a(n)/8^n = 7/sqrt(10). - _Amiram Eldar_, May 05 2023

%p [seq(n*binomial(2*n, n)*fib(n), n=0..27)];

%t Table[n Binomial[2n,n]Fibonacci[n],{n,0,20}] (* _Harvey P. Dale_, Oct 22 2011 *)

%Y Cf. A000984, A000045.

%K nonn,easy

%O 0,2

%A _Zerinvary Lajos_, Jun 09 2006