Numerators of a sequence of fractions converging to e.

Terms

a(0) =3a(1) =5a(2) =19a(3) =49a(4) =193a(5) =685a(6) =2721a(7) =12341a(8) =49171a(9) =271801a(10) =1084483a(11) =7073725a(12) =28245729a(13) =212385209a(14) =848456353a(15) =7226001865a(16) =28875761731a(17) =274743964621