The Belgian 2.5 euro coin is a commemorative euro coin valid in Belgium first issued in 2015 with 70,000 coins minted. The coin commemorates the 200th anniversary of Napoleon's defeat in the Battle of Waterloo.
Belgium originally planned to mint €2 commemorative coins for the occasion. This plan was blocked by France, however (after 180,000 of the coins had already been minted, they had to be discarded). Printing in the 2.5 euro denomination gets around the ability of France to veto production as they will not be legal tender in the European Union, they are only legal for currency in Belgium. EU law states that any country can issue any new coins it wants as long as they are in an irregular denomination, so it invented a €2.5 coin.
References
Belgian 2.5 euro coin Wikipedia(Text) CC BY-SA