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

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =5a(5) =31a(6) =127a(7) =393a(8) =1037a(9) =2665a(10) =7591a(11) =24443a(12) =81731a(13) =264837a(14) =820275a(15) =2478841a(16) =7522349a(17) =23301765a(18) =73463257a(19) =232730545a(20) =733726155a(21) =2298299319a(22) =7181056499a(23) =22484743007a(24) =70688617451a(25) =222916145131a(26) =703639618241