B737 Captain reported the right pack was inoperative and while following the after-takeoff checklist with the bleeds off as required by the MEL; the aircraft was depressurized for a short period of time while climbing.

Narrative

This aircraft had a right Air Conditioning (AC) pack that was inoperative. The release had several steps associated with configuring this panel during several phases of flight. The MEL required takeoff and landing to be bleeds off.The operation was normal until the after takeoff checklist. Following the steps for the right pack inoperative; there was a short period of time that the aircraft was climbing while depressurized.Maybe Boeing did a copy/paste and didn't think about reversing switches? The left pack inoperative would have a slightly different procedure; however; because the isolation valve remains open. So it's not exactly a mirror image procedure.Following the MEL steps for the right pack inoperative; the isolation valve is closed; so when I turn the engine 2 bleed air on; it doesn't do anything. The next step is turning the APU bleed air off; which is what started the depressurization. I paused for a couple seconds to allow some stabilization like would be done in a normal bleeds off takeoff.After realizing the issue; I quickly turned the engine 1 bleed air switch on. The aircraft began pressurizing again; and there was no further issue.For the right pack inoperative after takeoff checklist; the engine bleed air switches should've been reversed. Yes; engine 1 bleed air and APU bleed air would be on at the same time potentially causing the dual bleed air light. However; this is addressed in the notes of the MEL already so Boeing is aware and is OK with this light for a few seconds that it might be illuminated.The risk here is something like this happening at a high elevation airport and triggering the CABIN ALTITUDE warning.There's one other minor issue that could be addressed as well. For the landing checklist; it tells us to turn the APU bleed air on. However; there's no mention of turning the APU on prior to that point. So here's another potential of depressurization.