Problem Statement

You are given a positive integer n, representing total orders where each order consists of a pickup and a delivery service.

Count all valid pickup/delivery sequences such that delivery(x) is always after of pickup(x).

Return the answer modulo 10^9 + 7.

Examples

• Example 1:

  • Input: n = 1
  • Expected Output: 1
  • Justification: With just one order, there's only one valid sequence: pickup and then delivery. Thus, the expected output is 1.

• Example 2:

  • Input: n = 2
  • Expected Output: 6
  • Justification: With two orders, there are six valid sequences: P1 D1 P2 D2, P1 P2 D1 D2, P1 P2 D2 D1, P2 D2 P1 D1, P2 P1 D1 D2, P2 P1 D2 D1. Therefore, the expected output is 6.

• Example 3:

  • Input: n = 5
  • Expected Output: 113400
  • Justification: For five orders, the number of valid sequences increases significantly because each additional order adds complexity to how pickups and deliveries can be arranged. The expected output for three orders is 113400.

Try it yourself

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