Binomial transform of the continued fraction expansion of e.

Terms

a(0) =2a(1) =3a(2) =6a(3) =12a(4) =23a(5) =46a(6) =98a(7) =213a(8) =458a(9) =972a(10) =2051a(11) =4322a(12) =9098a(13) =19113a(14) =40054a(15) =83748a(16) =174767a(17) =364086a(18) =757298a(19) =1572861a(20) =3262242a(21) =6757500a(22) =13981019a(23) =28894090a(24) =59652314a(25) =123032913a(26) =253522382a(27) =521957844a(28) =1073741831a(29) =2207135966