a(n) = Sum_{i=1..n} i*(n-i)^i.

Terms

a(0) =0a(1) =1a(2) =4a(3) =14a(4) =50a(5) =187a(6) =738a(7) =3084a(8) =13652a(9) =63917a(10) =315736a(11) =1641314a(12) =8956110a(13) =51175799a(14) =305527878a(15) =1901829488a(16) =12319405728a(17) =82896050937a(18) =578485474092