%I #10 Jan 18 2022 02:30:38

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

%C Reduction of a function f(x) by a substitution q(x)->s(x) is introduced at A193010.

%F From _Amiram Eldar_, Jan 18 2022: (Start)

%F Equals Sum_{k>=0} 2^(2*k+1)*Fibonacci(2*k+1)/(2*k+1)!.

%F Equals 2*cosh(1)*sinh(sqrt(5))/sqrt(5). (End)

%e 6.3830192266109834906946736316102032592390...

%t f[x_] := Sinh[2 x]; r[n_] := Fibonacci[n];

%t c[n_] := SeriesCoefficient[Series[f[x], {x, 0, n}], n]

%t u1 = N[Sum[c[n]*r[n], {n, 0, 100}], 100]

%t RealDigits[u1, 10]

%Y Cf. A000045, A193010, A192232, A193079.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Jul 15 2011