a(n) = N(6,n), where N(6,x) is the 6th Narayana polynomial.

Terms

a(0) =1a(1) =132a(2) =903a(3) =3304a(4) =8925a(5) =20076a(6) =39907a(7) =72528a(8) =123129a(9) =198100a(10) =305151a(11) =453432a(12) =653653a(13) =918204a(14) =1261275a(15) =1698976a(16) =2249457a(17) =2933028a(18) =3772279a(19) =4792200a(20) =6020301a(21) =7486732a(22) =9224403a(23) =11269104a(24) =13659625a(25) =16437876a(26) =19649007a(27) =23341528a(28) =27567429