Linear Algebraic Approach to Formulate A New Recurrence Relation for Bernoulli Numbers from the Power-Sum of Natural Numbers with Experiments on Pedagogy

In this article, a new recurrence relation formula for Bernoulli numbers have been derived, and sum of integer exponents of natural numbers has been revisited from this novel perspective. Some interesting pedagogical experiments on wording and presentation of mathematical derivation have been attempted, and development from first principle have been undertaken in line with this experimental approach.