Three combinatorial sums involving central binomial coefficients

Key Points

• The study develops recursive expressions for combinatorial sums involving central binomial coefficients and harmonic numbers.
• Recursive expressions were derived using summation by parts for three classes of sums involving various harmonic numbers.
• An alternative method was presented to show closed forms of certain sums in terms of Stirling numbers and r-Stirling numbers.
• The implications of these findings enhance understanding of relationships between different classes of sums in combinatorial mathematics.