a(n) = s(n+3)/5, where s is A024729.

Terms

a(0) =1a(1) =1a(2) =1a(3) =6a(4) =11a(5) =16a(6) =46a(7) =106a(8) =216a(9) =501a(10) =1111a(11) =2751a(12) =6266a(13) =14281a(14) =33721a(15) =80766a(16) =189436a(17) =439981a(18) =1037826a(19) =2544951a(20) =6062726a(21) =14300776a(22) =34248926a(23) =84236481a(24) =202586011a(25) =484002391a(26) =1166815571a(27) =2886959131a(28) =6992716766a(29) =16840627851