Is there a database for sequences indexed by partitions similar to Sloane's OEIS? I mean, I am aware that in the OEIS there are some arrays indexed by partitions, but I feel as though most of such sequences that frequently appear in combinatorial literature are not there. 


One example of a sequence I'd really like to recognise begins as follows: 


$a[1]=1$, 


$a[2]=a[1^2]=2$, 


$a[3]=a[1^3]=4$, $a[2,1]=8$, 


$a[4]=a[1^4]=8$, $a[3,1]=a[2,1^2]=16$, $a[2^2]=24$, 


$a[5]=a[1^5]=16$, $a[4,1]=a[2,1^3]=32$, $a[3,2]=a[2^2,1]=52$, $a[3,1^2]=48$. 


The obvious patterns $a[\lambda]=a[\lambda^t]$ and $a[n]=2^{n-1}$, $a[n-1,1]=2^n$ do hold in general, if it helps.



Databases for sequences indexed by partitions
Thanks for asking this question! It really is a perfect occation for me advertising (once again) the combinatorial statistic finder <http://www.FindStat.org>!


To search the database for partitions, see <http://www.FindStat.org/StatisticFinder/IntegerPartitions>


