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This document presents a study of the integer sequence A200144, which counts the number of multinomial coefficients that are evenly divisible by k based on partitions of n into k parts. The author defines relevant notation and concepts. Two main theorems are presented. Theorem 1 proves that a certain expression involving multinomial coefficients and integer sequences is always an integer. Theorem 2 proves that the expression of a multinomial coefficient divided by k is always an integer for any partition.
- Author
- db
- Language
- EN