a(n) = 55*(n+1)*binomial(n+3,11)/3.

Terms

a(0) =165a(1) =2200a(2) =15730a(3) =80080a(4) =325325a(5) =1121120a(6) =3403400a(7) =9335040a(8) =23556390a(9) =55426800a(10) =122862740a(11) =258658400a(12) =520550030a(13) =1006778080a(14) =1879537000a(15) =3399510400a(16) =5975701875a(17) =10236025800a(18) =17125658550a(19) =28042014000a(20) =45017447475a(21) =70963464000a(22) =109993369200a(23) =167844019200