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

Terms

a(0) =0a(1) =1a(2) =3a(3) =12a(4) =64a(5) =441a(6) =3855a(7) =41464a(8) =533736a(9) =8071785a(10) =141351715a(11) =2829417276a(12) =64038928728