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

Terms

a(0) =1a(1) =3a(2) =11a(3) =45a(4) =195a(5) =873a(6) =3989a(7) =18483a(8) =86515a(9) =408105a(10) =1936881a(11) =9238023a(12) =44241261a(13) =212601015a(14) =1024642875a(15) =4950790605a(16) =23973456915a(17) =116312293305a(18) =565280386625