a(n) = binomial(n+3, 3)*(1 + binomial(n+2, 3)/4).

Terms

a(0) =1a(1) =5a(2) =20a(3) =70a(4) =210a(5) =546a(6) =1260a(7) =2640a(8) =5115a(9) =9295a(10) =16016a(11) =26390a(12) =41860a(13) =64260a(14) =95880a(15) =139536a(16) =198645a(17) =277305a(18) =380380a(19) =513590a(20) =683606a(21) =898150a(22) =1166100a(23) =1497600a(24) =1904175a(25) =2398851a(26) =2996280a(27) =3712870a(28) =4566920a(29) =5578760