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

Terms

a(0) =1a(1) =3a(2) =9a(3) =29a(4) =96a(5) =319a(6) =1059a(7) =3513a(8) =11651a(9) =38640a(10) =128149a(11) =425007a(12) =1409541a(13) =4674761a(14) =15503904a(15) =51418891a(16) =170531391a(17) =565569477a(18) =1875718199a(19) =6220842720a(20) =20631502201a(21) =68424633483a(22) =226931147409a(23) =752619970949