Square table, read by antidiagonals, where T(n,k) = C((n+1)*2^(k-1), k) for n>=0, k>=0.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =2a(5) =1a(6) =1a(7) =3a(8) =6a(9) =4a(10) =1a(11) =4a(12) =15a(13) =56a(14) =70a(15) =1a(16) =5a(17) =28a(18) =220a(19) =1820a(20) =4368a(21) =1a(22) =6a(23) =45a(24) =560a(25) =10626a(26) =201376a(27) =906192a(28) =1a(29) =7