a(n) = Sum_{k=0..n} binomial(n+2*k,n-k) * Fibonacci(k+1).

Terms

a(0) =1a(1) =2a(2) =7a(3) =28a(4) =112a(5) =442a(6) =1733a(7) =6785a(8) =26569a(9) =104069a(10) =407677a(11) =1597049a(12) =6256294a(13) =24508321a(14) =96008389a(15) =376101237a(16) =1473331342a(17) =5771598891a(18) =22609547282a(19) =88570192914a(20) =346963118658