a(n) = (1/4) * Sum_{k=0..n} (k+2) * binomial(2*k+2,2*n-2*k+1).

Terms

a(0) =1a(1) =3a(2) =9a(3) =30a(4) =91a(5) =271a(6) =801a(7) =2330a(8) =6710a(9) =19172a(10) =54386a(11) =153362a(12) =430257a(13) =1201685a(14) =3343079a(15) =9268130a(16) =25614741a(17) =70595817a(18) =194078465a(19) =532337092a(20) =1457119612a(21) =3980884648a(22) =10856936212a(23) =29562266740a(24) =80375490401a(25) =218228740855a(26) =591758714965