Summary: Lengyel introduced a sequence of numbers $Z_{n}$, defined combinatorially, that satisfy a recurrence where the coefficients are Stirling numbers of the second kind. He proved some 2-adic properties of these numbers. In this paper, we give another recurrence for the sequence $Z_{n}$, where the coefficients are Stirling numbers of the first kind. Using this formula, we give another proof of Lengyel's lower bound on the 2-adic valuation of the $Z_{n}$. We also resolve some conjectures of Lengyel about the sequence $Z_{n}$.

11B73, 11F85

lengyel's sequence, Stirling number, congruence, p-adic property