SQL Query to determine number of tables

Firstly its very important to tell us if you are using a vintage version of SQL Server. A lot has changed since 2000!

Secondly, really you are going about obtaining your data the wrong way. You are trying to combine 2 sets of data which aren't related. The correct way to handle this is to pull 2 datasets, 1 with the number of tables (Gordon has already provided this), and one with the aggregated values per table (which you already have). If for some reason you really can't do this then see the option below using a simple sub-query.

SQL Server - Window Functions Not Supported

Use a simple sub-query, being careful to duplicate the where clauses.

SELECT TableNumber AS TAFEL
    , COUNT (*) AS AANTAL
    , ObjectDescription AS PRODUCT
    , (
      SELECT COUNT(DISTINCT TableNumber) 
      FROM TableMemory 
      WHERE ObjectType IN (1, 17)
    ) TableCount
FROM TableMemory 
WHERE ObjectType IN (1, 17)
GROUP BY TableNumber, ObjectType, ObjectDescription
ORDER BY TableNumber;

SQL Server - Window Functions Supported

With reference to Gordon's existing answer to a similar question (which I admit could be hard to translate, hence why I haven't flagged as a duplicate), you can do it as follows.

1. Compute a row number partitioned by TableNumber.
2. Count how many rows with row number = 1 there are. Because row number 1 will only exist once per TableNumber. Note I do this in a CROSS APPLY to avoid duplicating the logic twice, once in the SELECT and once in the GROUP BY.

WITH cte AS (
  SELECT TableNumber AS TAFEL
      , ObjectDescription AS PRODUCT
      , ROW_NUMBER() OVER (PARTITION BY TableNumber ORDER BY ObjectDescription) rn
  FROM TableMemory T
  WHERE ObjectType IN (1, 17)
)
SELECT TAFEL, PRODUCT
    , COUNT (*) AS AANTAL
    , SUM(RowToCount) OVER () TableCount
FROM cte
CROSS APPLY (VALUES (CASE WHEN rn = 1 THEN 1 ELSE 0 END)) AS X (RowToCount)
GROUP BY TAFEL, PRODUCT, RowToCount
ORDER BY TAFEL;

Assuming that "tafel" is table, then just use count(distinct):

SELECT COUNT(DISTINCT TableNumber) 
FROM TableMemory 
WHERE ObjectType IN (1, 17);

If you want your original data with the number of distinct tables, then just add dense_rank() twice:

SELECT TableNumber AS TAFEL, COUNT (*) AS AANTAL,
       ObjectDescription AS PRODUCT,
       (-1 +
        DENSE_RANK() OVER (ORDER BY TableNumber ASC) +
        DENSE_RANK() OVER (ORDER BY TableNumber DESC)
       ) as num_tables
FROM TableMemory 
WHERE (ObjectType = 1 OR ObjectType = 17)
GROUP BY TableNumber, ObjectType, ObjectDescription
ORDER BY TableNumber;