Number triangle T(n,k)=(-1)^(n-k)*(3k+2)*C(3n+1, n-k)/(2n+k+2).

Terms

a(0) =1a(1) =-2a(2) =1a(3) =7a(4) =-5a(5) =1a(6) =-30a(7) =25a(8) =-8a(9) =1a(10) =143a(11) =-130a(12) =52a(13) =-11a(14) =1a(15) =-728a(16) =700a(17) =-320a(18) =88a(19) =-14a(20) =1a(21) =3876a(22) =-3876a(23) =1938a(24) =-627a(25) =133a(26) =-17a(27) =1a(28) =-21318a(29) =21945