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

Terms

a(0) =1a(1) =2a(2) =7a(3) =31a(4) =142a(5) =659a(6) =3113a(7) =14918a(8) =72199a(9) =351983a(10) =1726022a(11) =8504509a(12) =42070429a(13) =208812722a(14) =1039387519a(15) =5186451311a(16) =25935769702a(17) =129942777227a(18) =652133298421