T(n, k) = [x^k] (1/2 - x)^(-n) - (1 - x)^(-n).

Terms

a(0) =0a(1) =1a(2) =3a(3) =3a(4) =14a(5) =45a(6) =7a(7) =45a(8) =186a(9) =630a(10) =15a(11) =124a(12) =630a(13) =2540a(14) =8925a(15) =31a(16) =315a(17) =1905a(18) =8925a(19) =35770a(20) =128898a(21) =63a(22) =762a(23) =5355a(24) =28616a(25) =128898a(26) =515844a(27) =1891890a(28) =127a(29) =1785