a(n) = (n+1)(n+2)^3*(n+3)^2*(n+4)(n^2 + 4n + 5)/1440.

Terms

a(0) =1a(1) =30a(2) =340a(3) =2275a(4) =10878a(5) =41160a(6) =131040a(7) =365310a(8) =916575a(9) =2110966a(10) =4528524a(11) =9150505a(12) =17568460a(13) =32272800a(14) =57041664a(15) =97454268a(16) =161556525a(17) =260710590a(18) =410664100a(19) =632879247a(20) =956166442a(21) =1418672200a(22) =2070276000a(23) =2975456250a(24) =4216691115