If this question is dumb please excuse me. 


Does this type of partition have a name and if so, what is it?


A sequence of partitions of an integer $\vec{\lambda}\_1, \vec{\lambda}\_2,....\vec{\lambda}\_j $ such that the tuple of weights $(|\vec{\lambda}\_1|,|\vec{\lambda}\_2|,.... |\vec{\lambda}\_j|)$ forms a partition of a fixed integer $n.$ 



Does this type of partition have a name?
These are counted in [OEIS A001970](http://oeis.org/A001970) where they are called "partitions of partitions" along with some other interpretations. As Simon noted, they do differ from the more-studied plane partitions.


