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We study the interplay between recurrences for zeta related functions atinteger values, `Minor Corner Lattice' Toeplitz determinants and integercomposition based sums. Our investigations touch on functional identities dueto Ramanujan and Grosswald, the transcendence of the zeta function at oddinteger values, the Li Criterion for the Riemann Hypothesis andpseudo-characteristic polynomials for zeta related functions. We begin with arecent result for \zeta(2s) and some seemingly new Bernoulli relations, whichwe use to obtain a generalised Ramanujan polynomial and properties thereof.

A trio of Bernoulli relations, their implications for the Ramanujan polynomials and the zeta constants