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

Terms

a(0) =1a(1) =3a(2) =10a(3) =38a(4) =150a(5) =592a(6) =2325a(7) =9110a(8) =35679a(9) =139748a(10) =547425a(11) =2144474a(12) =8400768a(13) =32909089a(14) =128917478a(15) =505018715a(16) =1978350057a(17) =7749948948a(18) =30359496230a(19) =118929689144a(20) =465892807802