Triangle read by rows, T(n,k) = (n!)^3 * [x^k] [z^n] hypergeom([], [1, 1], z)^x for n>=0, 0<=k<=n.

Terms

a(0) =1a(1) =0a(2) =1a(3) =0a(4) =-3a(5) =4a(6) =0a(7) =46a(8) =-81a(9) =36a(10) =0a(11) =-1899a(12) =3916a(13) =-2592a(14) =576a(15) =0a(16) =163476a(17) =-375375a(18) =305500a(19) =-108000a(20) =14400a(21) =0a(22) =-25333590a(23) =63002191a(24) =-58725000a(25) =26370000a(26) =-5832000a(27) =518400a(28) =0a(29) =6412369860