cp's OEIS Frontend

A193028 Decimal expansion of the coefficient of x in the reduction of e^(2x) by x^2->x+1.

%I A193028 #10 Jan 18 2022 02:28:56
%S A193028 1,1,2,4,4,2,8,9,3,6,6,9,5,1,1,9,4,6,3,2,9,9,5,4,3,1,7,2,9,2,7,5,1,2,
%T A193028 6,9,7,1,4,1,4,5,0,3,1,5,0,4,1,3,9,6,8,1,8,6,5,5,5,5,7,7,3,1,9,9,0,8,
%U A193028 8,6,8,5,9,4,9,9,6,6,0,1,0,6,0,4,7,2,4,7,3,5,5,4,6,1,7,9,1,2,4,7
%N A193028 Decimal expansion of the coefficient of x in the reduction of e^(2x) by x^2->x+1.
%C A193028 Reduction of a function f(x) by a substitution q(x)->s(x) is introduced at A193010.
%F A193028 From _Amiram Eldar_, Jan 18 2022: (Start)
%F A193028 Equals Sum_{k>=1} 2^k*Fibonacci(k)/k!.
%F A193028 Equals 2*e*sinh(sqrt(5))/sqrt(5). (End)
%e A193028 11.244289366951194632995431729275126971...
%t A193028 f[x_] := Exp[2 x]; r[n_] := Fibonacci[n];
%t A193028 c[n_] := SeriesCoefficient[Series[f[x], {x, 0, n}], n]
%t A193028 u1 = N[Sum[c[n]*r[n], {n, 0, 100}], 100]
%t A193028 RealDigits[u1, 10]
%Y A193028 Cf. A000045, A193010, A192232, A193027.
%K A193028 nonn,cons
%O A193028 2,3
%A A193028 _Clark Kimberling_, Jul 14 2011
%E A193028 Offset corrected by _Amiram Eldar_, Jan 18 2022