A team’s batting lineup may be truncated (by winning the game or by choosing not to bat any longer) at any point after the first pair starts batting. Now how many different sequences of partnerships...

A team’s batting lineup may be truncated (by winning the game or by choosing not to bat any longer) at any point after the first pair starts batting. Now how many different sequences of partnerships are possible? Here, it does matter whether one of the last two players gets out or not (but not which of the two was the one who got out).