a(n) = Sum_{k=0..n}(binomial(n-1,n-k)*binomial(n+k-1,n-k)).

Terms

a(0) =1a(1) =1a(2) =3a(3) =12a(4) =53a(5) =244a(6) =1152a(7) =5531a(8) =26875a(9) =131760a(10) =650492a(11) =3229368a(12) =16105344a(13) =80624935a(14) =404913225a(15) =2039146908a(16) =10293657125a(17) =52071019600a(18) =263888886528