a(n) = (n + 1)*(n^2 + 2)*(n^3 + 3)/6.

Terms

a(0) =1a(1) =4a(2) =33a(3) =220a(4) =1005a(5) =3456a(6) =9709a(7) =23528a(8) =50985a(9) =101260a(10) =187561a(11) =328164a(12) =547573a(13) =877800a(14) =1359765a(15) =2044816a(16) =2996369a(17) =4291668a(18) =6023665a(19) =8303020a(20) =11260221a(21) =15047824a(22) =19842813a(23) =25849080a(24) =33300025a(25) =42461276a(26) =53633529a(27) =67155508a(28) =83407045a(29) =102812280