Inverse binomial transform of a math magic problem.

Terms

a(0) =1a(1) =1a(2) =4a(3) =6a(4) =14a(5) =26a(6) =54a(7) =106a(8) =214a(9) =426a(10) =854a(11) =1706a(12) =3414a(13) =6826a(14) =13654a(15) =27306a(16) =54614a(17) =109226a(18) =218454a(19) =436906a(20) =873814a(21) =1747626a(22) =3495254a(23) =6990506a(24) =13981014a(25) =27962026a(26) =55924054a(27) =111848106a(28) =223696214a(29) =447392426