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

Terms

a(0) =1a(1) =1a(2) =2a(3) =2a(4) =5a(5) =13a(6) =6a(7) =16a(8) =43a(9) =116a(10) =24a(11) =66a(12) =182a(13) =503a(14) =1393a(15) =120a(16) =336a(17) =942a(18) =2644a(19) =7429a(20) =20894a(21) =720a(22) =2040a(23) =5784a(24) =16410a(25) =46586a(26) =132329a(27) =376093a(28) =5040a(29) =14400