Wolfram Function Repository (Under Development)
Instantuse addon functions for the Wolfram Language
Get the list of lists whose entries are the hook lengths of the entries of a Young diagram
ResourceFunction["HookLengths"][p] gives a list of lists of lengths p, for a partition p, where an entry is the hook length of the corresponding cell in the Young diagram of p. 
Here is a partition :
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This is its Ferrers diagram:
In[2]:= 

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These are the hook lengths for the shape p:
In[3]:= 

Out[3]= 

This is used to format a Young diagram:
In[4]:= 

The Young diagram with shape p:
In[5]:= 

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A hook of length 5:
In[6]:= 

Out[6]= 

The hook lengths of p:
In[7]:= 

Out[7]= 

The number of standard Young tableaux for the diagram of shape p:
In[8]:= 

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