Triangle read by rows, T(n,k) = (binomial(n,k)^3 - binomial(n,k))/6 for k=1..n-1 and n >= 2.

Terms

a(0) =1a(1) =4a(2) =4a(3) =10a(4) =35a(5) =10a(6) =20a(7) =165a(8) =165a(9) =20a(10) =35a(11) =560a(12) =1330a(13) =560a(14) =35a(15) =56a(16) =1540a(17) =7140a(18) =7140a(19) =1540a(20) =56a(21) =84a(22) =3654a(23) =29260a(24) =57155a(25) =29260a(26) =3654a(27) =84a(28) =120a(29) =7770