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

Terms

a(0) =1a(1) =0a(2) =0a(3) =2a(4) =5a(5) =9a(6) =18a(7) =40a(8) =88a(9) =189a(10) =405a(11) =872a(12) =1880a(13) =4050a(14) =8721a(15) =18781a(16) =40450a(17) =87120a(18) =187632a(19) =404105a(20) =870329a(21) =1874448a(22) =4037040a(23) =8694658a(24) =18725869a(25) =40330305a(26) =86860242a(27) =187072760a(28) =402902600a(29) =867739941