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

Terms

a(0) =1a(1) =1a(2) =3a(3) =2a(4) =5a(5) =13a(6) =6a(7) =14a(8) =33a(9) =79a(10) =24a(11) =54a(12) =122a(13) =277a(14) =633a(15) =120a(16) =264a(17) =582a(18) =1286a(19) =2849a(20) =6331a(21) =720a(22) =1560a(23) =3384a(24) =7350a(25) =15986a(26) =34821a(27) =75973a(28) =5040a(29) =10800