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) =0a(3) =2a(4) =14a(5) =40a(6) =85a(7) =194a(8) =531a(9) =1488a(10) =3933a(11) =10078a(12) =26068a(13) =68503a(14) =180428a(15) =472781a(16) =1235331a(17) =3230628a(18) =8460734a(19) =22162520a(20) =58026826a(21) =151889301a(22) =397612420a(23) =1040994327a(24) =2725491954a(25) =7135481535a(26) =18680634840a(27) =48906105174a(28) =128038194911a(29) =335209825828