T(n, k) = binomial(n, k)*hypergeom([(1 - n)/2, -n/2], [1], 4).

Terms

a(0) =1a(1) =1a(2) =1a(3) =3a(4) =6a(5) =3a(6) =7a(7) =21a(8) =21a(9) =7a(10) =19a(11) =76a(12) =114a(13) =76a(14) =19a(15) =51a(16) =255a(17) =510a(18) =510a(19) =255a(20) =51a(21) =141a(22) =846a(23) =2115a(24) =2820a(25) =2115a(26) =846a(27) =141a(28) =393a(29) =2751