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

Terms

a(0) =1a(1) =1a(2) =5a(3) =2a(4) =9a(5) =41a(6) =6a(7) =26a(8) =113a(9) =493a(10) =24a(11) =102a(12) =434a(13) =1849a(14) =7889a(15) =120a(16) =504a(17) =2118a(18) =8906a(19) =37473a(20) =157781a(21) =720a(22) =3000a(23) =12504a(24) =52134a(25) =217442a(26) =907241a(27) =3786745a(28) =5040a(29) =20880