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Rational sums of inverse powers of fixed points of e
#15
This is indeed an interesting connection.
Now my quick 2 cents about it.

First, we want the explicit function of which the sums of the powers of the inverted fixed points are the coefficients. We compare Jay's beginnin with index 1 in the first row with Sloane's beginning at index 1 in the second row:

Obviously we have to move the lower row to the left which is the same as dividing Sloane's function by . We get then

and see that the sign is swapped for each uneven power, which can be achieved by using instead of .
So we get
with .



for . If we transform this further via we get
to prove.

Looks strange, perhaps I made an error somewhere.
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