Hickerson series of almost integers

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This page is the answer to the task Hickerson series of almost integers in the Rosetta Code.

Description (from Rosetta Code)

The following function, due to D Hickerson, is said to generate "Almost integers" by the "Almost Integer" page of Wolfram Mathworld. (December 31 2013).

The function is:

It is said to produce "almost integers" for n between 1 and 17. The purpose of the task is to verify this assertion.

Assume that an "almost integer" has either a nine or a zero as its first digit after the decimal point of its decimal string representation

The task is to calculate all values of the function checking and stating which are "almost integers".

Note: Use extended/arbitrary precision numbers in your calculation if necessary to ensure you have adequate precision of results as for example:

h(18) = 3385534663256845326.39...