A193084 - OEIS

%I #9 Oct 23 2015 02:35:53

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

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

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

%N Decimal expansion of the coefficient of x in 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 -0.3029588714336260011975849802354811365293918921...

%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, A193083.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Jul 15 2011