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

Terms

a(0) =1a(1) =3a(2) =10a(3) =47a(4) =350a(5) =3825a(6) =54306a(7) =932155a(8) =18641526a(9) =424703541a(10) =10849407082a(11) =307010484775