a(n) = (n+1)*(n+2)*(n+3)*(11*n^2 + 29*n + 20)/120.

Terms

a(0) =1a(1) =12a(2) =61a(3) =206a(4) =546a(5) =1232a(6) =2478a(7) =4572a(8) =7887a(9) =12892a(10) =20163a(11) =30394a(12) =44408a(13) =63168a(14) =87788a(15) =119544a(16) =159885a(17) =210444a(18) =273049a(19) =349734a(20) =442750a(21) =554576a(22) =687930a(23) =845780a(24) =1031355a(25) =1248156a(26) =1499967a(27) =1790866a(28) =2125236a(29) =2507776