G.f. is (1-S)/(1+S), where S = g.f. for A000084.

Terms

a(0) =1a(1) =-2a(2) =-2a(3) =-2a(4) =-6a(5) =-10a(6) =-34a(7) =-82a(8) =-254a(9) =-730a(10) =-2238a(11) =-6826a(12) =-21370a(13) =-67122a(14) =-213654a(15) =-684258a(16) =-2208694a(17) =-7169298a(18) =-23402738a(19) =-76748130a(20) =-252790518a(21) =-835816658a(22) =-2773236614a(23) =-9230776706a(24) =-30814377058a(25) =-103139338858a(26) =-346067984622