Calculating
Many of the numbers on this website do not have a known closed-form formula, meaning there isn't a "nice" expression where you can plug in n/k/r. If they are not already calculated and made available on the OEIS or the linked articles, your best bet would be to extract the coefficients off the provided egf using a computer algebra program like Mathematica.
If you prefer traditional programming, you can have a go at implementing the recurrences in your programming language of choice. If you do this, consider making it open-source and sending me a link, so I can add it to the corresponding section.
If you can't find the numbers and are not able to calculate them, feel free to reach out and I will try to help. I'd be very interested in hearing about what applications you found. My e-mail is on the bottom of the home page.
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