Sample from Binomial(n, p) whose mean equals 1 / (1 - p)

Discussion is on going for this closed question: Binomial distribution in R. We want to draw samples from a Binomial(n, p) whose mean equals 1 / (1 - p).

I decide to open a new question because:

1. the original one was closed for lack of clarity;

2. I am assuming that I have understood the original poster correctly.

As stated, the description of the problem is very clear now. Write an R function to get such samples.