cp's OEIS Frontend

A193017 Decimal expansion of the constant term of the reduction of cosh(x) by x^2->x+1.

%I A193017 #13 Jan 18 2022 02:36:34
%S A193017 1,5,9,0,6,0,9,7,5,6,4,0,6,4,6,1,4,6,2,9,6,9,7,9,3,1,1,9,9,9,9,5,8,2,
%T A193017 9,1,6,5,1,8,3,5,3,6,7,5,0,3,1,0,6,0,7,0,6,1,3,5,5,4,1,8,1,3,4,7,4,4,
%U A193017 4,6,7,8,3,2,3,6,8,4,4,5,1,0,5,4,2,3,3,7,6,6,0,4,2,0,0,7,9,8,4,8
%N A193017 Decimal expansion of the constant term of the reduction of cosh(x) by x^2->x+1.
%C A193017 Reduction of a function f(x) by a substitution q(x)->s(x) is introduced at A193010.
%F A193017 From _Amiram Eldar_, Jan 18 2022: (Start)
%F A193017 Equals 1 + Sum_{k>=1} Fibonacci(2*k-1)/(2*k)!.
%F A193017 Equals (2 * cosh(phi) + (3+sqrt(5))*cosh(1/phi))/(5+sqrt(5)), where phi is the golden ratio (A001622). (End)
%e A193017 1.5906097564064614629697931199995829165183536750...
%t A193017 f[x_] := Cosh[x]; r[n_] := Fibonacci[n];
%t A193017 c[n_] := SeriesCoefficient[Series[f[x], {x, 0, n}], n]
%t A193017 u0 = N[Sum[c[n]*r[n - 1], {n, 0, 300}], 100]
%t A193017 RealDigits[u0, 10]
%Y A193017 Cf. A000045, A001622, A193010, A192232, A193025.
%K A193017 nonn,cons
%O A193017 1,2
%A A193017 _Clark Kimberling_, Jul 14 2011