Triangle S(n,k) by rows: coefficients of 3^(n/2)*(x^(2/3)*d/dx)^n when n=0,2,4,6,...

Terms

a(0) =1a(1) =1a(2) =3a(3) =4a(4) =24a(5) =9a(6) =28a(7) =252a(8) =189a(9) =27a(10) =280a(11) =3360a(12) =3780a(13) =1080a(14) =81a(15) =3640a(16) =54600a(17) =81900a(18) =35100a(19) =5265a(20) =243a(21) =58240a(22) =1048320a(23) =1965600a(24) =1123200a(25) =252720a(26) =23328a(27) =729a(28) =1106560a(29) =23237760