Central (C-)Bernoulli Numbers Arising from the MVDC Method

This note introduces a new class of "central Bernoulli numbers", denoted C_r(n), which arise naturally from the cascade coefficients of the Moment-Centred Decomposition (MVDC) method. It provides a proof that these numbers can be expressed in a closed form using Nörlund's generalised Bernoulli polynomials. A compact exponential generating function for C_r(n) is derived, and their relationship to the classical Bernoulli numbers is shown in the n→∞ limit. The paper serves as a self-contained analytic appendix to the main MVDC paper, anchoring the method in the classical theory of special polynomials.