a(n) = Sum_{k=0..floor(n/5)} (-1)^k * binomial(n+4,5*k+4) * Catalan(k).

Terms

a(0) =1a(1) =5a(2) =15a(3) =35a(4) =70a(5) =125a(6) =200a(7) =275a(8) =275a(9) =0a(10) =-999a(11) =-3610a(12) =-9380a(13) =-20570a(14) =-39440a(15) =-65251a(16) =-85695a(17) =-56435a(18) =141735a(19) =781770a(20) =2413128a(21) =5999325a(22) =12921350a(23) =24387900a(24) =39098925a(25) =46638744a(26) =11740695a(27) =-158571665a(28) =-674961760a(29) =-1956733020