The small leg of the integral triangle

This small Table gives the sides a, b  
in the triangle with  hypotenuse c =

      n         a           b       c
      1          3          4     5
      2          7        24    25
      3        44       117  125
      4      336       527  625
      5      237     3116 3125
     6   10296    11753  5^6
     7   16124    76443  5^7
     8 164833   354144  5^8

For each n (that is for each hypotenuse c = ),
there are exactly n pairs of integer sides a and b.
In the Table, for each n I show only new "solution",
that is new pair of values of sides which is not
proportional to some previous values.
In other words, each new line present new
integral triangle not similar to previous ones.
The interesting problem is the function a(n)
(or b(n)). It's still not-known to me...