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

Terms

a(0) =1a(1) =1a(2) =2a(3) =19a(4) =110a(5) =476a(6) =2477a(7) =15093a(8) =86830a(9) =485290a(10) =2826902a(11) =16857116a(12) =100034453a(13) =594833357a(14) =3574477090a(15) =21611465819a(16) =130955824174a(17) =796195223398