cp's OEIS Frontend

A193014 Decimal expansion of the coefficient of x in the reduction of cos(x) by x^2->x+1.

%I A193014 #10 Jan 18 2022 02:35:25
%S A193014 3,8,5,6,0,5,1,3,7,9,5,5,7,4,8,8,2,9,1,5,1,3,2,4,3,5,9,1,7,2,1,3,2,5,
%T A193014 0,1,0,3,5,4,6,4,1,1,1,4,3,9,7,4,7,2,5,0,9,0,5,2,9,4,8,7,1,8,9,0,0,3,
%U A193014 6,1,0,6,6,5,7,7,4,8,6,5,8,3,1,4,8,2,7,5,8,8,7,3,0,4,5,4,8,3,3,6
%N A193014 Decimal expansion of the coefficient of x in the reduction of cos(x) by x^2->x+1.
%C A193014 Reduction of a function f(x) by a substitution q(x)->s(x) is introduced at A193010.
%F A193014 From _Amiram Eldar_, Jan 18 2022: (Start)
%F A193014 Equals Sum_{k>=1} (-1)^k*Fibonacci(2*k)/(2*k)!.
%F A193014 Equals -2*sin(1/2)*sin(sqrt(5)/2)/sqrt(5). (End)
%e A193014 -0.3856051379557488291513243591721325...
%t A193014 f[x_] := Cos[x]; r[n_] := Fibonacci[n];
%t A193014 c[n_] := SeriesCoefficient[Series[f[x], {x, 0, n}], n]
%t A193014 u1 = N[Sum[c[n]*r[n], {n, 0, 300}], 100]
%t A193014 RealDigits[u1, 10]
%Y A193014 Cf. A000045, A193010, A192232, A193014.
%K A193014 nonn,cons
%O A193014 0,1
%A A193014 _Clark Kimberling_, Jul 14 2011