Triangle read by rows: T(n,k) = (-1)^(n+k)*(n+k+1)*binomial(n,k)*binomial(n+k,k) for n >= k >= 0.

Terms

a(0) =1a(1) =-2a(2) =6a(3) =3a(4) =-24a(5) =30a(6) =-4a(7) =60a(8) =-180a(9) =140a(10) =5a(11) =-120a(12) =630a(13) =-1120a(14) =630a(15) =-6a(16) =210a(17) =-1680a(18) =5040a(19) =-6300a(20) =2772a(21) =7a(22) =-336a(23) =3780a(24) =-16800a(25) =34650a(26) =-33264a(27) =12012a(28) =-8a(29) =504