co.combinatorics - Combinatorial sequences whose ratios $a_{n+1}/a_{n}$ are integers.

Let a_n be the largest power of 2 that divides R_n, the number of reduced Latin squares of order n. We know the value of a_n for n≤11 (see this for example). The sequence begins (1,1,1,2²,2³,2⁶,2¹⁰,2¹⁷,2²¹,2²⁸,2³⁵,...) for n≥1.

I wouldn't conjecture that a_n+1/a_n is always an integer (although, it seems plausible). However, we do know that a_n+1/a_n is an integer for 1≤n≤10.