By means of the generating function approach, we derive several summation formulae involving multiple harmonic numbers Hn,ℓ (σ), as well as other combinatorial numbers named after Bernoulli, Euler, Bell, Genocchi and Stirling.

Motivated by a problem proposed by Seiffert a quarter of century ago, we explicitly evaluate binomial sums with Pell and Lucas polynomials as weight functions. Their special cases result in several interesting identities concerning Fibonacci and Lucas numbers.

Seven infinite series involving two free variables and central binomial coefficients (in denominators) are explicitly evaluated in closed form. Several identities regarding Pell/Lucas polynomials and Fibonacci/Lucas numbers are presented as consequences.