A general two-term recurrence and its solution

We find a general explicit formula for all sequences satisfying a two-term recurrence of a certain kind. This generalizes familiar formulas for the Stirling and Lah numbers.

► A formula for certain two-term recurrent sequences is derived.
► Our study generalizes familiar formulas for the Stirling and Lah numbers.
► Our results are proved algebraically and use the Lagrange interpolation formula.