Array read by antidiagonals: T(n,k) = Sum_{i=1..n} binomial(1+i,2)^k.

Terms

a(0) =0a(1) =0a(2) =1a(3) =0a(4) =1a(5) =2a(6) =0a(7) =1a(8) =4a(9) =3a(10) =0a(11) =1a(12) =10a(13) =10a(14) =4a(15) =0a(16) =1a(17) =28a(18) =46a(19) =20a(20) =5a(21) =0a(22) =1a(23) =82a(24) =244a(25) =146a(26) =35a(27) =6a(28) =0a(29) =1