Upper (3/2)-midsequence of binomial(n,3) and binomial(n,2); see Comments.

Terms

a(0) =0a(1) =0a(2) =2a(3) =6a(4) =15a(5) =30a(6) =53a(7) =84a(8) =126a(9) =180a(10) =248a(11) =330a(12) =429a(13) =546a(14) =683a(15) =840a(16) =1020a(17) =1224a(18) =1454a(19) =1710a(20) =1995a(21) =2310a(22) =2657a(23) =3036a(24) =3450a(25) =3900a(26) =4388a(27) =4914a(28) =5481a(29) =6090