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%I #11 Jan 18 2022 02:30:50
%S 4,8,6,1,2,7,0,1,4,0,3,4,0,2,1,1,1,4,2,3,0,0,7,5,8,0,9,7,6,6,4,9,2,3,
%T 7,1,2,1,7,5,4,3,9,0,0,6,8,9,0,7,1,9,8,6,0,7,7,7,3,2,1,0,7,2,6,6,0,4,
%U 0,0,8,4,1,0,3,2,7,5,0,7,6,8,4,6,2,7,2,8,9,6,0,3,3,8,7,7,4,4,0,3
%N Decimal expansion of the coefficient of x in the reduction of cosh(2x) 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} 2^(2*k)*Fibonacci(2*k)/(2*k)!.
%F Equals 2*sinh(1)*sinh(sqrt(5))/sqrt(5). (End)
%e 4.86127014034021114230075809766492371...
%t f[x_] := Cosh[2 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, 100}], 100]
%t RealDigits[u1, 10]
%Y Cf. A000045, A193010, A192232, A193081.
%K nonn,cons
%O 1,1
%A _Clark Kimberling_, Jul 15 2011
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