a(n) = 10*binomial(2*n + 1, n - 4)/(n + 6).

Terms

a(0) =1a(1) =10a(2) =65a(3) =350a(4) =1700a(5) =7752a(6) =33915a(7) =144210a(8) =600875a(9) =2466750a(10) =10015005a(11) =40320150a(12) =161280600a(13) =641886000a(14) =2544619500a(15) =10056336264a(16) =39645171810a(17) =155989499540a(18) =612815891050