# 1,2,4,8,16,31,57,99,…

another awesome crescent sequence to try its sum-series of reciprocals. Check at A000127 of the Oeis. It has a beautiful connection with the Pascal’s triangle. Its generating function is

$\frac{1-3x+4x^2-2x^3+x^4}{(1-x)^5}$

What is the g.f. of the reciprocals?