Triangle where T(n,k)=2*T(n,k-1)+C(n-1,k)-C(n-1,k-1) and n>=k>=0.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =2a(5) =3a(6) =1a(7) =3a(8) =5a(9) =9a(10) =1a(11) =4a(12) =8a(13) =14a(14) =27a(15) =1a(16) =5a(17) =12a(18) =22a(19) =41a(20) =81a(21) =1a(22) =6a(23) =17a(24) =34a(25) =63a(26) =122a(27) =243a(28) =1a(29) =7