cp's OEIS Frontend

A193015 Decimal expansion of the constant term of the reduction of sinh(x) by x^2->x+1.

%I A193015 #10 Jan 18 2022 02:36:21
%S A193015 1,9,3,3,1,3,2,3,9,9,0,6,4,1,7,3,0,4,8,7,6,4,4,3,7,9,6,0,9,0,5,8,8,0,
%T A193015 5,5,9,9,1,9,4,4,9,3,1,3,0,7,3,5,1,4,7,2,5,7,1,4,5,8,9,2,3,2,1,5,0,7,
%U A193015 9,1,9,0,7,6,5,1,8,5,7,4,3,0,0,5,9,2,3,9,0,4,6,3,6,6,3,9,6,0,4,6
%N A193015 Decimal expansion of the constant term of the reduction of sinh(x) by x^2->x+1.
%C A193015 Reduction of a function f(x) by a substitution q(x)->s(x) is introduced at A193010.
%F A193015 From _Amiram Eldar_, Jan 18 2022: (Start)
%F A193015 Equals Sum_{k>=1} Fibonacci(2*k)/(2*k+1)!.
%F A193015 Equals (2 * sinh(phi) - (3+sqrt(5))*sinh(1/phi))/(5+sqrt(5)), where phi is the golden ratio (A001622). (End)
%e A193015 0.1933132399064173048764437960905880...
%t A193015 f[x_] := Sinh[x]; r[n_] := Fibonacci[n];
%t A193015 c[n_] := SeriesCoefficient[Series[f[x], {x, 0, n}], n]
%t A193015 u0 = N[Sum[c[n]*r[n - 1], {n, 0, 300}], 100]
%t A193015 RealDigits[u0, 10]
%Y A193015 Cf. A000045, A001622, A193010, A192232, A193016.
%K A193015 nonn,cons
%O A193015 0,2
%A A193015 _Clark Kimberling_, Jul 14 2011