Number of colored integer partitions of 2n using all colors of an n-set such that parts i have distinct color patterns in arbitrary order and each pattern for a part i has i colors in (weakly) increasing order.

A327681

Number of colored integer partitions of 2n using all colors of an n-set such that parts i have distinct color patterns in arbitrary order and each pattern for a part i has i colors in (weakly) increasing order.