a(n) = (15*n^2+45*n-70)*binomial(n+4,6)/8.

Terms

a(0) =0a(1) =0a(2) =10a(3) =175a(4) =1225a(5) =5565a(6) =19425a(7) =56595a(8) =144375a(9) =332475a(10) =705705a(11) =1401400a(12) =2632630a(13) =4718350a(14) =8121750a(15) =13498170a(16) =21754050a(17) =34118490a(18) =52229100a(19) =78233925a(20) =114911335a(21) =165809875a(22) =235410175a(23) =329311125a(24) =454442625a(25) =619307325a(26) =834253875a(27) =1111784310