Triangle read by rows: T(n, k) = 3^n*Sum_{j=0..k} (-1)^(k - j)*binomial(k, j) * Pochhammer(j/3, n).

Terms

a(0) =1a(1) =0a(2) =1a(3) =0a(4) =4a(5) =2a(6) =0a(7) =28a(8) =24a(9) =6a(10) =0a(11) =280a(12) =320a(13) =144a(14) =24a(15) =0a(16) =3640a(17) =5040a(18) =3120a(19) =960a(20) =120a(21) =0a(22) =58240a(23) =92960a(24) =71280a(25) =30720a(26) =7200a(27) =720a(28) =0a(29) =1106560