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<p>We develop arithmetic terms that express partial sums of binomial coefficients, and we extend the method to obtain arithmetic terms for multisections of such sums. Furthermore, we present an arithmetic term for a specific family of multinomial coefficient sums, which in particular yields an arithmetic term for the central trinomial coefficients. This result provides a solution to an open problem from the classic text “Concrete Mathematics,” which remained unresolved for around three decades.</p>

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Arithmetic terms for sums of multinomial coefficients

  • 期刊论文

  • 发表日期：

    2025年11月6日

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  • Joseph M. Shunia,
  • Lorenzo Sauras Altuzarra

摘要

We develop arithmetic terms that express partial sums of binomial coefficients, and we extend the method to obtain arithmetic terms for multisections of such sums. Furthermore, we present an arithmetic term for a specific family of multinomial coefficient sums, which in particular yields an arithmetic term for the central trinomial coefficients. This result provides a solution to an open problem from the classic text “Concrete Mathematics,” which remained unresolved for around three decades.