NAME
    euler - Euler number

SYNOPSIS
    euler(n)

TYPES
    n           integer, n <= 1000000 if even

    return      integer

DESCRIPTION
    Returns the Euler number with index n, i.e. the coefficient E_n in
    the expansion

                sech(t) = Sigma E_n * t^n/n!

    When euler(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 euler(k) with 0 <= k <= n will be executed quickly.
    If euler(k) is called with negative k, zero is returned and the
    memory used by the table iu freed.

    Considerable runtime and memory are required for calculating
    euler(n) for large even n.

EXAMPLE
    ; for (n = 0; n <= 6; n++) print euler(n),; print;
    1 0 -1 0 5 0 -61

LIMITS
    none

LINK LIBRARY
    NUMBER *qeuler(long n)

SEE ALSO
    bernoulli, bell, catalan, comb, fact, perm

## Copyright (C) 2000,2021  Ernest Bowen
##
## Calc is open software; you can redistribute it and/or modify it under
## the terms of the version 2.1 of the GNU Lesser General Public License
## as published by the Free Software Foundation.
##
## Calc is distributed in the hope that it will be useful, but WITHOUT
## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
## Public License for more details.
##
## A copy of version 2.1 of the GNU Lesser General Public License is
## distributed with calc under the filename COPYING-LGPL.  You should have
## received a copy with calc; if not, write to Free Software Foundation, Inc.
## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
##
## Under source code control:   2000/12/14 01:33:00
## File existed as early as:    2000
##
## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
