a(n) = Sum_{k=2..n} n(n-1)...(n-k+1)/k.

Terms

a(0) =0a(1) =1a(2) =5a(3) =20a(4) =84a(5) =409a(6) =2365a(7) =16064a(8) =125664a(9) =1112073a(10) =10976173a(11) =119481284a(12) =1421542628a(13) =18348340113a(14) =255323504917