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A193086 Decimal expansion of the coefficient of x in the reduction of (e^x)*sin(x) by x^2->x+1.

%I A193086 #5 Mar 30 2012 18:57:38
%S A193086 2,3,9,2,5,2,8,6,5,9,2,7,2,4,2,9,0,9,7,3,8,7,4,9,2,1,1,6,5,8,9,2,2,7,
%T A193086 7,1,9,8,4,9,9,5,5,0,1,4,5,3,6,9,6,8,6,8,6,9,2,7,7,4,8,7,9,3,5,5,3,7,
%U A193086 5,2,1,7,6,8,8,0,0,2,3,7,4,2,1,2,5,7,9,4,2,1,4,5,3,5,9,1,0,0,8,1
%N A193086 Decimal expansion of the coefficient of x in the reduction of (e^x)*sin(x) by x^2->x+1.
%C A193086 Reduction of a function f(x) by a substitution q(x)->s(x) is introduced at A193010.
%e A193086 2.3925286592724290973874921165892277198499...
%t A193086 f[x_] := Exp[x] Sin[x]; r[n_] := Fibonacci[n];
%t A193086 c[n_] := SeriesCoefficient[Series[f[x], {x, 0, n}], n]
%t A193086 u0 = N[Sum[c[n]*r[n - 1], {n, 0, 100}], 100]
%t A193086 RealDigits[u0, 10]  (* A193085 *)
%t A193086 u1 = N[Sum[c[n]*r[n], {n, 0, 100}], 100]
%t A193086 RealDigits[u1, 10]  (* A193086 *)
%Y A193086 Cf. A193010, A192232, A193085.
%K A193086 nonn,cons
%O A193086 1,1
%A A193086 _Clark Kimberling_, Jul 15 2011