a(n) = Sum_{k=0..n} (-1)^(n-k)*k*Stirling2(n,k).

Terms

a(0) =0a(1) =1a(2) =1a(3) =-2a(4) =-1a(5) =11a(6) =-18a(7) =-41a(8) =317a(9) =-680a(10) =-1767a(11) =19911a(12) =-68264a(13) =-59643a(14) =2076973a(15) =-11905466a(16) =18577387a(17) =269836343a(18) =-2819431570a(19) =12357816867a(20) =17355428041a(21) =-752675321800