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%I #9 Oct 23 2015 02:35:59
%S 2,5,2,0,5,8,9,8,4,0,6,6,7,7,5,3,6,2,7,4,2,5,8,4,7,7,8,2,5,2,4,7,8,2,
%T 9,4,3,6,5,9,0,9,7,1,1,8,9,8,5,9,3,9,3,2,8,1,9,7,8,4,2,6,4,8,5,2,3,1,
%U 6,8,8,8,4,8,6,2,8,1,9,2,3,3,5,3,8,7,9,8,3,3,1,7,6,1,6,8,7,5,2,1
%N Decimal expansion of the constant term of the reduction of (e^x)*cos(x) by x^2->x+1.
%C Reduction of a function f(x) by a substitution q(x)->s(x) is introduced at A193010.
%e constant=0.25205898406677536274258477825247829436590...
%t f[x_] := Exp[x] Cos[x]; r[n_] := Fibonacci[n];
%t c[n_] := SeriesCoefficient[Series[f[x], {x, 0, n}], n]
%t u0 = N[Sum[c[n]*r[n - 1], {n, 0, 100}], 100]
%t RealDigits[u0, 10] (* A193083 *)
%t u1 = N[Sum[c[n]*r[n], {n, 0, 100}], 100]
%t RealDigits[u1, 10] (* A193084 *)
%Y Cf. A193010, A192232, A193084.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Jul 15 2011
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