return sumOfProductsOfDeltas / (count() - 1);
  }

  /**
   * Returns the <a href="http://mathworld.wolfram.com/CorrelationCoefficient.html">Pearson's or
   * product-moment correlation coefficient</a> of the values. The count must greater than one, and
   * the {@code x} and {@code y} values must both have non-zero population variance (i.e. {@code

        assertWithMessage("Pearson's correlation coefficient of " + values)
            .that(pearsonsCorrelationCoefficient)
            .isNaN();
        assertWithMessage("Pearson's correlation coefficient by addAll(PairedStats) of " + values)
            .that(pearsonsCorrelationCoefficient)
            .isNaN();
      } else {
        assertWithMessage("Pearson's correlation coefficient of " + values)

        assertWithMessage("Pearson's correlation coefficient of " + values)
            .that(pearsonsCorrelationCoefficient)
            .isNaN();
        assertWithMessage("Pearson's correlation coefficient by addAll(PairedStats) of " + values)
            .that(pearsonsCorrelationCoefficient)
            .isNaN();
      } else {
        assertWithMessage("Pearson's correlation coefficient of " + values)

      if (values.hasAnyNonFinite()) {
        assertWithMessage("Pearson's correlation coefficient of " + values)
            .that(pearsonsCorrelationCoefficient)
            .isNaN();
      } else {
        assertWithMessage("Pearson's correlation coefficient of " + values)
            .that(pearsonsCorrelationCoefficient)
            .isWithin(ALLOWED_ERROR)
            .of(

      if (values.hasAnyNonFinite()) {
        assertWithMessage("Pearson's correlation coefficient of " + values)
            .that(pearsonsCorrelationCoefficient)
            .isNaN();
      } else {
        assertWithMessage("Pearson's correlation coefficient of " + values)
            .that(pearsonsCorrelationCoefficient)
            .isWithin(ALLOWED_ERROR)
            .of(

    return sumOfProductsOfDeltas / (count() - 1);
  }

  /**
   * Returns the <a href="http://mathworld.wolfram.com/CorrelationCoefficient.html">Pearson's or
   * product-moment correlation coefficient</a> of the values. The count must greater than one, and
   * the {@code x} and {@code y} values must both have non-zero population variance (i.e. {@code

            .size());

    // Almost force an overflow in the binomial coefficient calculation
    assertEquals(
        1391975640 /*C(34,14)*/,
        Collections2.orderedPermutations(concat(nCopies(20, 1), nCopies(14, 2))).size());
    // Do force an overflow in the binomial coefficient calculation
    assertEquals(
        Integer.MAX_VALUE,

            .size());

    // Almost force an overflow in the binomial coefficient calculation
    assertEquals(
        1391975640 /*C(34,14)*/,
        Collections2.orderedPermutations(concat(nCopies(20, 1), nCopies(14, 2))).size());
    // Do force an overflow in the binomial coefficient calculation
    assertEquals(
        Integer.MAX_VALUE,

        int m = (end + start) >>> 1;
        return listProduct(nums, start, m).multiply(listProduct(nums, m, end));
    }
  }

  /**
   * Returns {@code n} choose {@code k}, also known as the binomial coefficient of {@code n} and
   * {@code k}, that is, {@code n! / (k! (n - k)!)}.
   *
   * <p><b>Warning:</b> the result can take as much as <i>O(k log n)</i> space.
   *

    1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 * 10 * 11,
    1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 * 10 * 11 * 12
  };

  /**
   * Returns {@code n} choose {@code k}, also known as the binomial coefficient of {@code n} and
   * {@code k}, or {@link Integer#MAX_VALUE} if the result does not fit in an {@code int}.
   *
   * @throws IllegalArgumentException if {@code n < 0}, {@code k < 0} or {@code k > n}
   */