Inverse binomial transform of Thue-Morse sequence A001285.

Terms

a(0) =1a(1) =1a(2) =-1a(3) =0a(4) =3a(5) =-10a(6) =24a(7) =-48a(8) =83a(9) =-126a(10) =170a(11) =-208a(12) =240a(13) =-272a(14) =272a(15) =0a(16) =-1453a(17) =6698a(18) =-22050a(19) =60896a(20) =-148430a(21) =326404a(22) =-653280a(23) =1188640a(24) =-1939568a(25) =2730976a(26) =-2946256a(27) =1085760a(28) =5849808a(29) =-22935520