Sums of powers via central finite differences and Newton's formula

Abstract In this manuscript we derive formula for multifold sums of powers using Newton's formula and central differences. Related works Newton's interpolation formula and sums of powers (2025) Sums of powers via central finite differences and Newton's formula (2025) Sums of powers via backward finite differences and Newton's formula (2026) OEIS https://oeis.org/A387597 — Triangle read by rows: T(n,k) = Sum_{j=0..2k} (-1)^j * binomial(2k,j) * (0+k-j)^(2n). https://oeis.org/A392337 — Triangle read by rows: T(n,k) = Sum_{j=0..2k} (-1)^j * binomial(2k,j) * (1+k-j)^(2n). https://oeis.org/A390029 — Triangle read by rows: T(n,k) = Sum_{j=0..2k} (-1)^j * binomial(2k,j) * (2+k-j)^(2n). Metadata MSC2010: 05A19, 05A10, 41A15, 11B83 Keywords: Sums of powers, Newton's interpolation formula, Finite differences, Binomial coefficients, Faulhaber's formula, Bernoulli numbers, Bernoulli polynomials Interpolation, Approximation, Discrete convolution, Combinatorics, Polynomial identities, Central factorial numbers, Stirling numbers, Eulerian numbers, Worpitzky identity, Pascal's triangle, OEIS License: This work is licensed under a CC BY 4.0 License DOI: https://doi.org/10.5281/zenodo.18096789 Web Version: https://kolosovpetro.github.io/sums-of-powers-central-differences/ Sources: https://github.com/kolosovpetro/SumsOfPowersViaCentralFiniteDifferencesAndNewtonFormula ORCID: https://orcid.org/0000-0002-6544-8880 Email: kolosovp94@gmail.com