J. Cereceda

collaborators

4 papers

math.HO2026

The most concise recurrence formula for the sums of integer powers

JosÃ© L. Cereceda

For integers $n, k \geq 1$ , let $S_{k} (n)$ denote the power sum $1^{k} + 2^{k} + \dots + n^{k}$ . In this note, we first recall the minimal recurrence relation connecting $S_{k} (n)$ and $S_{k-…

math.CO2025

Formulas involving Cauchy polynomials, Bernoulli polynomials, and generalized Stirling numbers

JosÃ© L. Cereceda

In this paper, we derive novel formulas and identities connecting Cauchy numbers and polynomials with both ordinary and generalized Stirling numbers, binomial coefficients, central…

math.GM2025

A remark on an explicit formula for the sums of powers of integers

Recently, E. Samsonadze (arXiv:2411.11859v1) has given an explicit formula for the sums of powers of integers $S_{k} (n) = 1^{k} + 2^{k} + \dots + n^{k}$ . In this short note, we show that Sa…

math.GM2025

Sums of powers of integers and the sequence A304330

For integer $k \geq 1$ , let $S_{k} (n)$ denote the sum of the $k$ th powers of the first $n$ positive integers. In this paper, we derive a new formula expressing $2^{2 k}$ times $S_{2k}…