The naive implementation for your requirement would look like this:

record MyRecord( int a, int b )
{
  int hash; // Does not compile!!
  
  MyRecord
  {
    hash = a * 100 + b;
  }
       
  @Override
  public int hashCode() { return hash; }
}

When compiling that, JShell tells you:

|  Error:
|  field declaration must be static
|    (consider replacing field with record component)
|      int hash;
|          ^---^

Presumably, the error message returned by javac would look slightly different, but with more or less the same meaning: a record cannot have additional attributes other than the record components. And that would lead to a construct as shown in this answer.

If the hashcode calculation is really, really, REALLY time consuming, you can consider something like this:

record MyRecord( int a, int b )
{
  static final Map<MyRecord,Integer> hashes = new IdentityHashMap<>();
       
  public MyRecord
  {
    hashes.put( this, a * 100 + b );
  }
       
  @Override
  public int hashCode() { return hashes.get( this );}
}

But as this simple implementation is causing significant memory dissipation, you need to implement also a cleanup for the hashes map; otherwise an OutOfMemoryError will be thrown at some time …

A comment for the downvote would be appreciated.