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

Terms

a(0) =1a(1) =2a(2) =6a(3) =20a(4) =67a(5) =223a(6) =740a(7) =2454a(8) =8138a(9) =26989a(10) =89509a(11) =296858a(12) =984534a(13) =3265220a(14) =10829143a(15) =35914987a(16) =119112500a(17) =395038086a(18) =1310148722a(19) =4345124521a(20) =14410659481a(21) =47793131282a(22) =158506513926a(23) =525688823540