Triangle read by rows: T(n, k) = n! * 3^k * hypergeom([-k], [-n], 1/3).

Terms

a(0) =1a(1) =1a(2) =4a(3) =2a(4) =7a(5) =25a(6) =6a(7) =20a(8) =67a(9) =226a(10) =24a(11) =78a(12) =254a(13) =829a(14) =2713a(15) =120a(16) =384a(17) =1230a(18) =3944a(19) =12661a(20) =40696a(21) =720a(22) =2280a(23) =7224a(24) =22902a(25) =72650a(26) =230611a(27) =732529a(28) =5040a(29) =15840