a(n) = binomial(n+5,5)*(n+3)/3.

Terms

a(0) =1a(1) =8a(2) =35a(3) =112a(4) =294a(5) =672a(6) =1386a(7) =2640a(8) =4719a(9) =8008a(10) =13013a(11) =20384a(12) =30940a(13) =45696a(14) =65892a(15) =93024a(16) =128877a(17) =175560a(18) =235543a(19) =311696a(20) =407330a(21) =526240a(22) =672750a(23) =851760a(24) =1068795a(25) =1330056a(26) =1642473a(27) =2013760a(28) =2452472a(29) =2968064