Binomial transform of a fractal structured sequence.

Terms

a(0) =1a(1) =3a(2) =6a(3) =13a(4) =29a(5) =62a(6) =128a(7) =263a(8) =547a(9) =1148a(10) =2403a(11) =4977a(12) =10196a(13) =20764a(14) =42295a(15) =86505a(16) =177686a(17) =365590a(18) =750900a(19) =1535849a(20) =3126095a(21) =6338569a(22) =12829491a(23) =25978046a(24) =52704328a(25) =107181724a(26) =218353623a(27) =445043039a(28) =906192468a(29) =1841334795