a(n) = Sum_{k=0..floor(n^2/(2*n+1))} binomial(n * (n-2*k),k).

Terms

a(0) =1a(1) =1a(2) =1a(3) =4a(4) =9a(5) =26a(6) =91a(7) =281a(8) =1105a(9) =4105a(10) =16576a(11) =70643a(12) =301405a(13) =1382928a(14) =6363876a(15) =30605836a(16) =150820769a(17) =758835104a(18) =3941917840a(19) =20787546715a(20) =112615930451a(21) =620969188400