A Recursive Relation for Bipartition Numbers

We establish a recursive relation for the bipartition number p₂ (n) which might be regarded as an analogue of Euler's recursive relation for the partition number p (n). Two proofs of the main result are proved in this article. The first one is using the generating function, and the second one is using combinatoric objects (called ``symbols'') created by Lusztig for studying representation theory of finite classical groups.