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A119693
a(n) = binomial(2*n,n) * Fibonacci(n)/2.
1
0, 1, 3, 20, 105, 630, 3696, 22308, 135135, 826540, 5080790, 31391724, 194699232, 1211669900, 7561979100, 47310843600, 296633172465, 1863384566670, 11725074807600, 73889273973900, 466265883733650, 2945885346810120, 18632848373222460, 117972712180416600
OFFSET
0,3
FORMULA
a(n) = A119692(n)/2.
Sum_{n>=0} a(n)/8^n = 1/sqrt(10). - Amiram Eldar, May 04 2023
G.f.: (1+8*x-sqrt(1-4*x-16*x^2))/(2*sqrt(5)*sqrt(1-4*x-16*x^2)*sqrt(3+4*x+2*sqrt(1-4*x-16*x^2))). - Vladimir Kruchinin, Apr 29 2024
MAPLE
seq(binomial(2*n, n)*combinat[fibonacci](n)/2, n=0..27);
MATHEMATICA
a[n_] := Binomial[2*n, n] * Fibonacci[n] / 2; Array[a, 30, 0] (* Amiram Eldar, May 04 2023 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Zerinvary Lajos, Jun 09 2006
STATUS
approved