Summation formulae on reciprocal sequences

By means of series rearrangement, we prove an algebraic identity on the symmetric difference of bivariate Ω -polynomials associated with an arbitrary complex sequence. When the sequence concerned is ε -reciprocal, we find some unusual recurrence relations with binomial polynomials as coefficients. As applications, several interesting summation formulae are established for Bernoulli, Fibonacci, Lucas and Genocchi numbers.