a(n) = Sum_{k=0..floor(n/3)} (-1)^k * binomial(n+2,3*k+2) * Catalan(k).

Terms

a(0) =1a(1) =3a(2) =6a(3) =9a(4) =9a(5) =0a(6) =-26a(7) =-72a(8) =-117a(9) =-82a(10) =204a(11) =975a(12) =2289a(13) =3357a(14) =1332a(15) =-9834a(16) =-37935a(17) =-82593a(18) =-108282a(19) =2583a(20) =487521a(21) =1621071a(22) =3261546a(23) =3685230a(24) =-2318615a(25) =-24607854a(26) =-72887472a(27) =-134909701a(28) =-123941901a(29) =200330184