TreeFactorial on BinaryTree

The product, over the nodes, of the number of nodes at or below each.

On BinaryTree

Called as CombinatorialStat(x, "TreeFactorial"). The head's page has its examples.

Live

Distribution

Over BinaryTrees at each size, tallied here in your browser; sizes past 6 are not offered.

Sizes 1 to

Also on

The same name on other carriers, each its own implementation: OrderedTree.

FindStat St000411

The tree factorial of a binary tree.

Object	Value
[.,[.,.]]	2
[[.,.],.]	2
[.,[.,[.,.]]]	6
[.,[[.,.],.]]	6
[[.,.],[.,.]]	3
[[.,[.,.]],.]	6
[[[.,.],.],.]	6
[.,[.,[.,[.,.]]]]	24

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000411 has the rest.