OFFSET
1,2
COMMENTS
Reduction of a function f(x) by a substitution q(x)->s(x) is introduced at A193010.
FORMULA
From Amiram Eldar, Jan 19 2022: (Start)
Equals 1 + Sum_{k>=1} (-log(2))^k*Fibonacci(k-1)/k!.
Equals (4^(phi-1)*(5+3*sqrt(5)) + sqrt(5))/(5*phi*2^phi), where phi is the golden ratio (A001622). (End)
EXAMPLE
1.20062200396905852100739765904387826717805500...
MATHEMATICA
f[x_] := 2^(-x); r[n_] := Fibonacci[n];
c[n_] := SeriesCoefficient[Series[f[x], {x, 0, n}], n]
u0 = N[Sum[c[n]*r[n - 1], {n, 0, 100}], 100]
RealDigits[u0, 10]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Jul 14 2011
STATUS
approved