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IntegerPartitions[n, {k}]

series for x^(21)*(product 1/(1-x^i) for i=1 to 21) at x=0

partitions of 201 with 21 parts

import java.math.BigInteger;

public class Partitions {
  public BigInteger[][] array = new BigInteger[25][250];

  public Partitions() {
    int k, n;

    array[0][0] = BigInteger.ONE;
    
    for (n = 1; n < array[0].length; n++)
      array[0][n] = BigInteger.ZERO;

    for (k = 1; k < array.length; k++) {
      array[k][0] = BigInteger.ZERO;
      
      for (n = 1; n <= k; n++)
        array[k][n] = array[k-1][n-1];

      for (n = k+1; n < array[k].length; n++)
        array[k][n] = array[k-1][n-1].add(array[k][n-k]);
    }
  }

  public static void main(String[] args) {
    Partitions p = new Partitions();
    System.out.printf("p_{%d}(%d) = %s%n", 21, 201, p.array[21][201].toString());
  }
}