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