cp's OEIS Frontend

A193081 Decimal expansion of the constant term of the reduction of cosh(2x) by x^2->x+1.

%I A193081 #10 Jan 18 2022 02:30:21
%S A193081 4,8,7,0,7,1,8,6,3,3,4,0,0,8,0,5,7,3,6,8,5,6,6,5,9,4,2,1,1,3,7,7,7,5,
%T A193081 7,8,3,8,9,2,1,1,9,6,9,3,7,8,8,7,0,4,1,4,3,0,9,7,1,7,3,8,5,1,5,7,6,7,
%U A193081 2,4,3,5,4,5,0,3,5,8,8,6,3,2,8,3,5,4,0,4,1,7,6,6,9,6,5,9,4,2,5,0
%N A193081 Decimal expansion of the constant term of the reduction of cosh(2x) by x^2->x+1.
%C A193081 Reduction of a function f(x) by a substitution q(x)->s(x) is introduced at A193010.
%F A193081 From _Amiram Eldar_, Jan 18 2022: (Start)
%F A193081 Equals 1 + Sum_{k>=1} 2^(2*k)*Fibonacci(2*k-1)/(2*k)!.
%F A193081 Equals ((3+sqrt(5))*cosh(1-sqrt(5)) + 2*cosh(1+sqrt(5)))/(5 + sqrt(5)). (End)
%e A193081 4.8707186334008057368566594211377757838921196937...
%t A193081 f[x_] := Cosh[2 x]; r[n_] := Fibonacci[n];
%t A193081 c[n_] := SeriesCoefficient[Series[f[x], {x, 0, n}], n]
%t A193081 u0 = N[Sum[c[n]*r[n - 1], {n, 0, 100}], 100]
%t A193081 RealDigits[u0, 10]
%Y A193081 Cf. A000045, A193010, A192232, A193082.
%K A193081 nonn,cons
%O A193081 1,1
%A A193081 _Clark Kimberling_, Jul 15 2011