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

Terms

a(0) =1a(1) =2a(2) =8a(3) =33a(4) =138a(5) =581a(6) =2455a(7) =10395a(8) =44068a(9) =186953a(10) =793453a(11) =3368279a(12) =14300161a(13) =60713627a(14) =257763847a(15) =1094294875a(16) =4645306802a(17) =19717723173a(18) =83687094899a(19) =355155267179