Number triangle T(n,k) = [k<=n]*Hypergeometric2F1([-k, 2k-2n], [1], 2).

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =5a(5) =1a(6) =1a(7) =9a(8) =13a(9) =1a(10) =1a(11) =13a(12) =41a(13) =25a(14) =1a(15) =1a(16) =17a(17) =85a(18) =129a(19) =41a(20) =1a(21) =1a(22) =21a(23) =145a(24) =377a(25) =321a(26) =61a(27) =1a(28) =1a(29) =25