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MSE – Why am I finding the Catalan numbers in these "Snowball Numbers"?(math.meta.stackexchange.com)

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Link preview Mathematics Meta Stack Exchange Q&A about the site for people studying math at any level and professionals in related fields Mathematics Meta Stack Exchange · math.meta.stackexchange.com
I've been having fun trying to find new number systems that aren't in the OEIS. One such number system, is the "Snowball Numbers", which I will define below. Apologies if these have been

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