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

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =4a(5) =10a(6) =6a(7) =14a(8) =34a(9) =82a(10) =24a(11) =60a(12) =152a(13) =388a(14) =1000a(15) =120a(16) =312a(17) =816a(18) =2144a(19) =5656a(20) =14968a(21) =720a(22) =1920a(23) =5136a(24) =13776a(25) =37040a(26) =99808a(27) =269488a(28) =5040a(29) =13680