a(n) = n*(n+1)*(n^2 + 21*n + 50)/24.

Terms

a(0) =6a(1) =24a(2) =61a(3) =125a(4) =225a(5) =371a(6) =574a(7) =846a(8) =1200a(9) =1650a(10) =2211a(11) =2899a(12) =3731a(13) =4725a(14) =5900a(15) =7276a(16) =8874a(17) =10716a(18) =12825a(19) =15225a(20) =17941a(21) =20999a(22) =24426a(23) =28250a(24) =32500a(25) =37206a(26) =42399a(27) =48111a(28) =54375a(29) =61225