A193085 - OEIS

%I #6 Mar 30 2012 18:57:38

%S 1,1,6,6,3,4,7,3,4,8,1,9,0,8,6,4,5,4,0,4,8,1,3,2,1,6,5,5,4,7,0,2,0,1,

%T 7,2,3,9,5,9,3,0,1,2,3,1,1,8,9,4,4,5,7,2,1,4,3,5,9,2,0,7,2,5,7,0,8,4,

%U 1,5,3,4,1,0,5,8,7,1,2,2,6,8,7,1,3,1,6,0,4,9,7,5,9,5,2,9,9,3,6,1

%N Decimal expansion of the constant term of the reduction of (e^x)*sin(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=1.166347348190864540481321655470201723

%e ...

%t f[x_] := Exp[x] Sin[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]  (* A193085 *)

%t u1 = N[Sum[c[n]*r[n], {n, 0, 100}], 100]

%t RealDigits[u1, 10]  (* A193086 *)

%Y Cf. A193010, A192232, A193086.

%K nonn,cons

%O 1,3

%A _Clark Kimberling_, Jul 15 2011