a(n) = Sum_{k=0..n} binomial(n,k) * binomial(2*k,n-k).

Terms

a(0) =1a(1) =1a(2) =5a(3) =16a(4) =61a(5) =231a(6) =896a(7) =3515a(8) =13917a(9) =55501a(10) =222595a(11) =896930a(12) =3628120a(13) =14724022a(14) =59922175a(15) =244456581a(16) =999393021a(17) =4093381925a(18) =16793794625a(19) =69001682216a(20) =283889914171