a(n) = 1 - Sum_{k=2..n} k*k!.

Terms

a(0) =-3a(1) =-21a(2) =-117a(3) =-717a(4) =-5037a(5) =-40317a(6) =-362877a(7) =-3628797a(8) =-39916797a(9) =-479001597a(10) =-6227020797a(11) =-87178291197