a(n) = (n+1)*binomial(n+1,4).

Terms

a(0) =4a(1) =25a(2) =90a(3) =245a(4) =560a(5) =1134a(6) =2100a(7) =3630a(8) =5940a(9) =9295a(10) =14014a(11) =20475a(12) =29120a(13) =40460a(14) =55080a(15) =73644a(16) =96900a(17) =125685a(18) =160930a(19) =203665a(20) =255024a(21) =316250a(22) =388700a(23) =473850a(24) =573300a(25) =688779a(26) =822150a(27) =975415a(28) =1150720a(29) =1350360