Product_{n>=1} 1 / (1 - a(n)*x^n) = 1 + Sum_{n>=1} phi(n)*x^n, where phi = A000010.

Terms

a(0) =1a(1) =0a(2) =1a(3) =0a(4) =2a(5) =-3a(6) =4a(7) =-4a(8) =4a(9) =-10a(10) =14a(11) =-25a(12) =30a(13) =-48a(14) =48a(15) =-86a(16) =128a(17) =-192a(18) =286a(19) =-470a(20) =578a(21) =-1000a(22) =1386a(23) =-2423a(24) =3172a(25) =-5198a(26) =7102a(27) =-11994a(28) =16414a(29) =-25820