A119693 a(n) = binomial(2*n,n) * Fibonacci(n)/2.

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

Links

Table of n, a(n) for n=0..23.

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

Cf. A000045, A000984, A119692.

Sequence in context: A304494 A000917 A025535 * A158243 A139471 A154641

Adjacent sequences: A119690 A119691 A119692 * A119694 A119695 A119696

Keyword

easy,nonn

Author

Zerinvary Lajos, Jun 09 2006

Status

approved