}

    // Test validation with valid cron expressions
    public void test_validCronExpressions() {
        TestBean bean = new TestBean();

        // Test null value (should be valid)
        bean.setCronExpression(null);
        Set<ConstraintViolation<TestBean>> violations = validator.validate(bean);
        assertTrue(violations.isEmpty());

        // Test empty string (should be valid)

      assertThrows(IllegalArgumentException.class, () -> IntMath.binomial(n, 0));
    }
  }

  @AndroidIncompatible // slow
  @GwtIncompatible // java.math.BigInteger
  public void testMean() {
    // Odd-sized ranges have an obvious mean
    assertMean(2, 1, 3);

    assertMean(-2, -3, -1);
    assertMean(0, -1, 1);
    assertMean(1, -1, 3);
    assertMean((1 << 30) - 1, -1, Integer.MAX_VALUE);

    long sqrtMaxLong = (long) Math.sqrt(Long.MAX_VALUE);
    assertTrue(sqrtMaxLong <= LongMath.FLOOR_SQRT_MAX_LONG);
  }

  @AndroidIncompatible // slow
  @GwtIncompatible // java.math.BigInteger
  public void testMean() {
    // Odd-sized ranges have an obvious mean
    assertMean(2, 1, 3);

    assertMean(-2, -3, -1);
    assertMean(0, -1, 1);
    assertMean(1, -1, 3);
    assertMean((1L << 62) - 1, -1, Long.MAX_VALUE);