<image>Ancient Greek Pythagorean school mathematicians studied various polygonal numbers. For example, triangular numbers such as 1, 3, 6, 10, ..., the \(n\)th triangular number is \(\dfrac{n(n+1)}{2} = \dfrac{1}{2}n^2 + \dfrac{1}{2}n\). Let the \(n\)th \(k\)-polygonal number be \(N(n, k)\) \((k \geqslant 3)\), and the following are some formulas for the \(n\)th number of polygonal numbers in different shapes:

Triangular number______ \(N(n, 3) = \dfrac{1}{2}n^2 + \dfrac{1}{2}n\)  
Square number_________ \(N(n, 4) = n^2\)  
Pentagonal number______ \(N(n, 5) = \dfrac{3}{2}n^2 - \dfrac{1}{2}n\)  
Hexagonal number_______ \(N(n, 6) = 2n^2 - n\)  
___________________ and so on...

One can deduce the formula for \(N(n, k)\). From this, compute \(N(20, 32) =\) ____________.