cp's OEIS Frontend

A193080 Decimal expansion of the coefficient of x in the reduction of sinh(2x) by x^2->x+1.

%I A193080 #10 Jan 18 2022 02:30:38
%S A193080 6,3,8,3,0,1,9,2,2,6,6,1,0,9,8,3,4,9,0,6,9,4,6,7,3,6,3,1,6,1,0,2,0,3,
%T A193080 2,5,9,2,3,9,0,6,4,1,4,3,5,2,3,2,4,8,3,2,5,7,7,8,2,5,6,2,4,7,2,4,8,4,
%U A193080 6,7,7,5,3,9,6,3,8,5,0,2,9,2,0,0,9,7,4,4,5,9,4,2,7,9,1,3,8,0,7,1
%N A193080 Decimal expansion of the coefficient of x in the reduction of sinh(2x) by x^2->x+1.
%C A193080 Reduction of a function f(x) by a substitution q(x)->s(x) is introduced at A193010.
%F A193080 From _Amiram Eldar_, Jan 18 2022: (Start)
%F A193080 Equals Sum_{k>=0} 2^(2*k+1)*Fibonacci(2*k+1)/(2*k+1)!.
%F A193080 Equals 2*cosh(1)*sinh(sqrt(5))/sqrt(5). (End)
%e A193080 6.3830192266109834906946736316102032592390...
%t A193080 f[x_] := Sinh[2 x]; r[n_] := Fibonacci[n];
%t A193080 c[n_] := SeriesCoefficient[Series[f[x], {x, 0, n}], n]
%t A193080 u1 = N[Sum[c[n]*r[n], {n, 0, 100}], 100]
%t A193080 RealDigits[u1, 10]
%Y A193080 Cf. A000045, A193010, A192232, A193079.
%K A193080 nonn,cons
%O A193080 1,1
%A A193080 _Clark Kimberling_, Jul 15 2011