a(n) = Sum_{k=0..floor(n/4)} binomial(n+k,k)^2 * binomial(n-3*k,k).

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =26a(5) =73a(6) =148a(7) =257a(8) =2431a(9) =9676a(10) =26984a(11) =61993a(12) =332762a(13) =1487886a(14) =5029676a(15) =13986049a(16) =57394823a(17) =253491517a(18) =953613991a(19) =3032424076a(20) =11249004334a(21) =47032861778a(22) =185321607072a(23) =645015386921