Triangle read by rows: T(n, k) = n! * 2^k * hypergeom([-k], [-n], -1/2).

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =3a(5) =5a(6) =6a(7) =10a(8) =17a(9) =29a(10) =24a(11) =42a(12) =74a(13) =131a(14) =233a(15) =120a(16) =216a(17) =390a(18) =706a(19) =1281a(20) =2329a(21) =720a(22) =1320a(23) =2424a(24) =4458a(25) =8210a(26) =15139a(27) =27949a(28) =5040a(29) =9360