a(n) = Sum_{j=0..n} n^wt(j), where wt = A000120.

Terms

a(0) =1a(1) =2a(2) =5a(3) =16a(4) =29a(5) =66a(6) =127a(7) =512a(8) =737a(9) =1090a(10) =1541a(11) =3312a(12) =4369a(13) =7658a(14) =12209a(15) =65536a(16) =83537a(17) =105282a(18) =130987a(19) =167600a(20) =203701a(21) =254122a(22) =313259a(23) =649728a(24) =766201a(25) =912626a(26) =1079027a(27) =1778896a(28) =2071469a(29) =3081570