a(n) = n^4*(n^4-1)/240.

Terms

a(0) =0a(1) =0a(2) =1a(3) =27a(4) =272a(5) =1625a(6) =6993a(7) =24010a(8) =69888a(9) =179334a(10) =416625a(11) =893101a(12) =1791504a(13) =3398759a(14) =6148961a(15) =10678500a(16) =17895424a(17) =29065308a(18) =45916065a(19) =70764303a(20) =106666000a(21) =157594437a(22) =228648497a(23) =326294606a(24) =458645760a(25) =635781250a(26) =870110865a(27) =1176787521a(28) =1574172432a(29) =2084357107