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

Terms

a(0) =1a(1) =-1a(2) =-1a(3) =3a(4) =10a(5) =14a(6) =19a(7) =64a(8) =228a(9) =620a(10) =1488a(11) =3700a(12) =9845a(13) =26445a(14) =69490a(15) =180428a(16) =470197a(17) =1232747a(18) =3234809a(19) =8471680a(20) =22162520a(21) =57998169a(22) =151860644a(23) =397658788a(24) =1041115720a(25) =2725491954a(26) =7135163724a(27) =18680317029a(28) =48906619403a(29) =128039541180