MathNet 2006 — Part 04 Question 57

Find the number of 20-tuple $(p_1, p_2, \dots, p_{10}, q_1, q_2, \dots, q_{10})$ of positive integers with $p_1 = q_{10} = 1$ and $p_i+1 \lt q_i - p_i$ for all $i = 1, 2, \dots, 9$.