

A193082


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


2



4, 8, 6, 1, 2, 7, 0, 1, 4, 0, 3, 4, 0, 2, 1, 1, 1, 4, 2, 3, 0, 0, 7, 5, 8, 0, 9, 7, 6, 6, 4, 9, 2, 3, 7, 1, 2, 1, 7, 5, 4, 3, 9, 0, 0, 6, 8, 9, 0, 7, 1, 9, 8, 6, 0, 7, 7, 7, 3, 2, 1, 0, 7, 2, 6, 6, 0, 4, 0, 0, 8, 4, 1, 0, 3, 2, 7, 5, 0, 7, 6, 8, 4, 6, 2, 7, 2, 8, 9, 6, 0, 3, 3, 8, 7, 7, 4, 4, 0, 3
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OFFSET

1,1


COMMENTS

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


LINKS



FORMULA

Equals Sum_{k>=1} 2^(2*k)*Fibonacci(2*k)/(2*k)!.
Equals 2*sinh(1)*sinh(sqrt(5))/sqrt(5). (End)


EXAMPLE

4.86127014034021114230075809766492371...


MATHEMATICA

f[x_] := Cosh[2 x]; r[n_] := Fibonacci[n];
c[n_] := SeriesCoefficient[Series[f[x], {x, 0, n}], n]
u1 = N[Sum[c[n]*r[n], {n, 0, 100}], 100]
RealDigits[u1, 10]


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



