Don’t forget there are also around 400 or so uncommitted and unelected delegates chosen by the state parties. No first ballot majority, it’s wide open. Negotiated rather than brokered convention would probably be a better term. I don’t think many of the elected delegates will be for candidates over which the RNC has great sway. The top two or three will likely have to work it out amongst themselves.
The numbers I gave were only the committed delegates. I didn’t include any uncommitted ones.
Trump can win this quite easily without a single uncommitted delegate.