NAME
    bernoulli - Bernoulli number

SYNOPSIS
    bernoulli(n)

TYPES
    n		integer, n < 2^31 if even

    return	rational

DESCRIPTION
    Returns the Bernoulli number with index n, i.e. the coefficient B_n in
    the expansion

		t/(exp(t) - 1) = Sum B_n * t^n/n!

    bernoulli(n) is zero both for n < 0 and for n odd and > 2.
    When bernoulli(n) is computed for positive even n, the values for
    n and smaller positive even indices are stored in a table so that
    a later call to bernoulli(k) with 0 <= k < n will be executed quickly.

    Considerable runtime and memory are required for calculating
    bernoulli(n) for large even n.  For n = 1000, the numerator has
    1779 digits, the denominator 9 digits.

    The memory used to store calculated bernoulli numbers is freed by
    freebernoulli().

EXAMPLE
    > config("mode", "frac"),;
    > for (n = 0; n <= 6; n++) print bernoulli(n),; print;
    1 -1/2 1/6 0 -1/30 0 1/42

LIMITS
    n < 2^31-1

LIBRARY
    NUMBER *qbernoulli(long n)

SEE ALSO
    euler, catalan, comb, fact, perm