a(n) = binomial(n+4,4)*binomial(n+5,4)*binomial(n+6,4)/75.

Terms

a(0) =1a(1) =35a(2) =490a(3) =4116a(4) =24696a(5) =116424a(6) =457380a(7) =1557270a(8) =4723719a(9) =13026013a(10) =33157124a(11) =78835120a(12) =176729280a(13) =376375104a(14) =766192176a(15) =1498581756a(16) =2828205765a(17) =5168991135a(18) =9177226366a(19) =15870391460a(20) =26794167400a(21) =44253495000a(22) =71627692500a(23) =113794603650a(24) =177694650315