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

Terms

a(0) =1a(1) =4a(2) =14a(3) =52a(4) =202a(5) =794a(6) =3119a(7) =12229a(8) =47908a(9) =187656a(10) =735081a(11) =2879555a(12) =11280323a(13) =44189412a(14) =173106890a(15) =678125605a(16) =2656475662a(17) =10406424610a(18) =40765920840a(19) =159695609984a(20) =625588417786