Forest twice came from behind in the entertaining draw, with Ameobi scoring in each half for the home team.
At minute 20, he drew his team level with a brilliant effort into the top corner from the edge of the box and equalised again for Nottingham Forest nine minutes into the second half when his unstoppable shot from 25 yards beat the Swans goalkeeper.
Ameobi has been involved in all but one game played by Nottingham Forest in the Championship this season, and has contributed to 14 goals (5 goals, 9 assists).
In the Norwegian Eliteserien, Leke James continued his fine start to the season by netting twice for Molde in a 5-0 rout of Viking at the Aker Stadium.
James broke the deadlock when he converted a spot kick in the 5th minute and made it 3-0 in the 65th minute.
The 27-year-old has scored five goals in his first six appearances of the 2020 season.
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