%I #11 Jan 18 2022 02:30:07

%S 2,3,6,9,1,5,8,6,9,7,9,0,0,0,9,4,4,4,0,4,6,8,2,7,2,8,0,2,2,5,8,3,8,5,

%T 2,5,8,6,9,8,0,1,3,7,7,5,3,7,9,1,7,7,2,0,3,0,0,5,9,1,4,2,3,8,5,4,2,3,

%U 7,6,8,5,7,0,7,5,7,9,9,8,5,9,2,2,3,3,8,9,0,0,0,6,0,1,8,0,2,1,8,2

%N Decimal expansion of the constant term of 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>=1} 2^(2*k+1)*Fibonacci(2*k)/(2*k+1)!.

%F Equals ((3+sqrt(5))*sinh(1-sqrt(5)) + 2*sinh(1+sqrt(5)))/(5 + sqrt(5)). (End)

%e 2.3691586979000944404682728022583852586980...

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

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

%t u0 = N[Sum[c[n]*r[n - 1], {n, 0, 100}], 100]

%t RealDigits[u0, 10]

%Y Cf. A000045, A193010, A192232, A193080.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Jul 15 2011