Triangle read by rows: T(n, k) = n! * 4^k * hypergeom([-k], [-n], -1/4).

Terms

a(0) =1a(1) =1a(2) =3a(3) =2a(4) =7a(5) =25a(6) =6a(7) =22a(8) =81a(9) =299a(10) =24a(11) =90a(12) =338a(13) =1271a(14) =4785a(15) =120a(16) =456a(17) =1734a(18) =6598a(19) =25121a(20) =95699a(21) =720a(22) =2760a(23) =10584a(24) =40602a(25) =155810a(26) =598119a(27) =2296777a(28) =5040a(29) =19440