E.g.f.: 1/Product_{k>0} (1 - x^k/k)^k.

Terms

a(0) =1a(1) =1a(2) =4a(3) =18a(4) =114a(5) =810a(6) =7140a(7) =68880a(8) =766920a(9) =9304680a(10) =125086080a(11) =1814015280a(12) =28588356720a(13) =481128888240