G.f.: A(x) = 1 + x/exp( Sum_{k>=1} (A((-1)^k*x) - 1)^k/k ).

Terms

a(0) =1a(1) =1a(2) =1a(3) =-1a(4) =-3a(5) =1a(6) =9a(7) =1a(8) =-27a(9) =-13a(10) =81a(11) =67a(12) =-243a(13) =-285a(14) =729a(15) =1119a(16) =-2187a(17) =-4215a(18) =6561a(19) =15505a(20) =-19683a(21) =-56239a(22) =59049a(23) =202309a(24) =-177147a(25) =-724499a(26) =531441a(27) =2589521a(28) =-1594323a(29) =-9254363