a(n) = s(n+3)/5, where s is A024951.

Terms

a(0) =1a(1) =1a(2) =6a(3) =11a(4) =16a(5) =46a(6) =106a(7) =216a(8) =501a(9) =1111a(10) =3026a(11) =6941a(12) =16106a(13) =39571a(14) =102291a(15) =249886a(16) =593231a(17) =1466876a(18) =3784726a(19) =9385226a(20) =22941751a(21) =57430001a(22) =148203456a(23) =372194386a(24) =925716416a(25) =2325988621a(26) =6058260656a(27) =15328018016a(28) =38481839451a(29) =97762429061