Triangle read by rows: T(n, k) = n! * 3^k * hypergeom([-k], [-n], 2/3).

Terms

a(0) =1a(1) =1a(2) =5a(3) =2a(4) =8a(5) =34a(6) =6a(7) =22a(8) =82a(9) =314a(10) =24a(11) =84a(12) =296a(13) =1052a(14) =3784a(15) =120a(16) =408a(17) =1392a(18) =4768a(19) =16408a(20) =56792a(21) =720a(22) =2400a(23) =8016a(24) =26832a(25) =90032a(26) =302912a(27) =1022320a(28) =5040a(29) =16560