a(n) = Sum_{k=0..n} (-1)^k * binomial(n+4*k+4,n-k) * Catalan(k).

Terms

a(0) =1a(1) =4a(2) =7a(3) =5a(4) =4a(5) =29a(6) =50a(7) =-83a(8) =-185a(9) =743a(10) =1425a(11) =-5250a(12) =-9868a(13) =40530a(14) =73280a(15) =-319155a(16) =-557485a(17) =2573032a(18) =4341065a(19) =-21107670a(20) =-34398290a(21) =175655925a(22) =276438452a(23) =-1479202280a(24) =-2247154681a(25) =12581036223a(26) =18440253397a(27) =-107916225837a(28) =-152514334540a(29) =932452267956