Time perhaps to summarise this before closing, unless there are any more useful inputs?
a) Twins like Aztec, Cessna 310, Seneca etc takeoff every time with no ability to climb away if an engine is lost just after lift-off.
b) There is nothing to stop an A330 taking off on one engine if the runway is long enough. The power needs to be applied slowly and carefully until Vmcg is achieved when full power can be applied. There is significant strain on the nosewheel during the first part of the run.
c) It is EXTREMELY unlikely that this happened with this aircraft.
d) With 3 or more engines, an engine-out take-off is a specially trained and conducted manoeuvre and rarely flown.
e) There is a suggestion that at least one small twin has this manoeuvre in its Flight Manual.
Any more inputs?