a(n) = binomial(2n+1, n+1)*binomial(n+2, 2).

Terms

a(0) =1a(1) =9a(2) =60a(3) =350a(4) =1890a(5) =9702a(6) =48048a(7) =231660a(8) =1093950a(9) =5080790a(10) =23279256a(11) =105462084a(12) =473227300a(13) =2106121500a(14) =9307051200a(15) =40873466520a(16) =178520875830a(17) =775924068150