The number of partitions of $2n$ into partitions with no element greater than $n$ (copied and slightly adapted from http://mathworld.wolfram.com/PartitionFunctionq.html), so I'm looking for a nice formula of $q(2n,n)$.
By asking http://www.wolframalpha.com/input/?i=integer+partitions+of+12 and counting the ones of interest I get results from 2 to 12, that look the following: $ 1,3,7,15,30,58 $ which matches the data from http://oeis.org/A026820/table when you start from the $1$ in the 2.row and go straight down. My question is now, if there is closed formula or at least an asymptotic for $q(2n,n)$?