OFFSET
1,3
COMMENTS
Reduction of a function f(x) by a substitution q(x)->s(x) is introduced at A193010.
FORMULA
From Amiram Eldar, Jan 18 2022: (Start)
Equals 1 + Sum_{k>=1} Fibonacci(k-1)/(k!*2^k).
Equals exp(1/4)*(cosh(sqrt(5)/4) - sqrt(5)*sinh(sqrt(5)/4)/5). (End)
EXAMPLE
1.151945206759468821277485451505582743212385890...
MATHEMATICA
f[x_] := Exp[x/2]; 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