a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} 4^k * a(k) * a(n-2*k-1).

Terms

a(0) =1a(1) =1a(2) =1a(3) =5a(4) =9a(5) =29a(6) =65a(7) =437a(8) =953a(9) =3981a(10) =10097a(11) =49829a(12) =123241a(13) =516349a(14) =1400737a(15) =10203285a(16) =24698905a(17) =111642477a(18) =304787665a(19) =1704790917a(20) =4392726473a(21) =19951366877a(22) =56296655617a(23) =336083829621a(24) =878995865721