A119697 a(n) = Fibonacci(n)*n*binomial(2*n,n)/(n+1).
0, 1, 4, 30, 168, 1050, 6336, 39039, 240240, 1487772, 9237800, 57551494, 359444736, 2250244100, 14115694320, 88707831750, 558368324640, 3519726403710, 22215931214400, 140389620550410, 888125492826000, 5623962934819320, 35645449061816880, 226114365012465150
Offset: 0
Programs
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Maple
seq(binomial(2*n, n)*n*combinat[fibonacci](n)/(n+1), n=0..27);
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Mathematica
Table[Fibonacci[n]n Binomial[2n,n]/(n+1),{n,0,40}] (* Harvey P. Dale, Apr 29 2022 *)
Formula
a(n) = n * A119694(n).
Sum_{n>=0} a(n)/8^n = 7*sqrt(2/5) - 4. - Amiram Eldar, May 04 2023