a(n) = n*(n+1)*(n+2)*(n^2+2*n+17)/120.

Terms

a(0) =1a(1) =5a(2) =16a(3) =41a(4) =91a(5) =182a(6) =336a(7) =582a(8) =957a(9) =1507a(10) =2288a(11) =3367a(12) =4823a(13) =6748a(14) =9248a(15) =12444a(16) =16473a(17) =21489a(18) =27664a(19) =35189a(20) =44275a(21) =55154a(22) =68080a(23) =83330a(24) =101205a(25) =122031a(26) =146160a(27) =173971a(28) =205871a(29) =242296