a(n) = Sum_{i=0..n} i*L(i), where L = A000032.

Terms

a(0) =0a(1) =1a(2) =7a(3) =19a(4) =47a(5) =102a(6) =210a(7) =413a(8) =789a(9) =1473a(10) =2703a(11) =4892a(12) =8756a(13) =15529a(14) =27331a(15) =47791a(16) =83103a(17) =143810a(18) =247814a(19) =425445a(20) =727985a(21) =1241981a(22) =2113247a(23) =3587064a(24) =6075432a(25) =10269457a(26) =17326975a(27) =29185483a(28) =49083599a(29) =82429278