a(n) = Sum_{k=0..n} binomial(n-3,n-k)*Catalan(k).

Terms

a(0) =1a(1) =-1a(2) =2a(3) =5a(4) =19a(5) =75a(6) =305a(7) =1270a(8) =5390a(9) =23236a(10) =101480a(11) =448085a(12) =1997115a(13) =8973255a(14) =40602093a(15) =184853055a(16) =846206025a(17) =3892585325a(18) =17984308775a(19) =83417287855a(20) =388297304825