cp's OEIS Frontend

A193025 Decimal expansion of the coefficient of x in the reduction of cosh(x) by x^2->x+1.

%I A193025 #11 Jan 18 2022 02:28:35
%S A193025 6,3,6,6,4,7,4,0,5,9,6,7,3,6,9,1,9,0,3,6,9,7,8,1,1,3,4,3,9,9,3,6,7,3,
%T A193025 6,1,9,6,3,2,7,6,3,1,3,5,3,9,8,1,1,9,8,1,8,4,1,5,1,8,7,8,4,0,9,8,1,8,
%U A193025 7,0,4,7,6,1,0,3,0,9,5,3,3,4,9,2,9,9,2,2,5,4,8,9,2,3,7,1,0,9,5,0
%N A193025 Decimal expansion of the coefficient of x in the reduction of cosh(x) by x^2->x+1.
%C A193025 Reduction of a function f(x) by a substitution q(x)->s(x) is introduced at A193010.
%F A193025 From _Amiram Eldar_, Jan 18 2022: (Start)
%F A193025 Equals Sum_{k>=1} Fibonacci(2*k)/(2*k)!.
%F A193025 Equals (e-1)*sinh(sqrt(5)/2)/sqrt(5*e). (End)
%e A193025 0.6366474059673691903697811343993673619632...
%t A193025 f[x_] := Cosh[x]; r[n_] := Fibonacci[n];
%t A193025 c[n_] := SeriesCoefficient[Series[f[x], {x, 0, n}], n]
%t A193025 u1 = N[Sum[c[n]*r[n], {n, 0, 300}], 100]
%t A193025 RealDigits[u1, 10]
%Y A193025 Cf. A000045, A193010, A192232, A193017.
%K A193025 nonn,cons
%O A193025 0,1
%A A193025 _Clark Kimberling_, Jul 14 2011