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

Terms

a(0) =1a(1) =5a(2) =22a(3) =92a(4) =376a(5) =1518a(6) =6085a(7) =24285a(8) =96647a(9) =383911a(10) =1523117a(11) =6037745a(12) =23920853a(13) =94737897a(14) =375125126a(15) =1485173396a(16) =5879740780a(17) =23277813786a(18) =92160762514a(19) =364906983652