a(n) = Sum_{k=0..n} Fibonacci(n-k)*n^k.

Terms

a(0) =0a(1) =1a(2) =3a(3) =14a(4) =91a(5) =820a(6) =9650a(7) =140601a(8) =2440317a(9) =49109632a(10) =1123595495a(11) =28792920872a(12) =816742025772