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

Terms

a(0) =1a(1) =1a(2) =1a(3) =0a(4) =-3a(5) =-2a(6) =23a(7) =17a(8) =-333a(9) =86a(10) =6941a(11) =-17025a(12) =-160267a(13) =1082864a(14) =2273807a(15) =-56742606a(16) =152154285a(17) =2293098332a(18) =-22007462809a(19) =-15179437171