[[wp:Bernoulli number|Bernoulli numbers]] are used in some series expansions of several functions &nbsp; (trigonometric, hyperbolic, gamma, etc.), &nbsp; and are extremely important in number theory and analysis.

Note that there are two definitions of Bernoulli numbers; &nbsp; this task will be using the modern usage &nbsp; (as per &nbsp; ''The National Institute of Standards and Technology convention'').

The &nbsp; n<sup>th</sup> &nbsp; Bernoulli number is expressed as &nbsp; '''B'''<sub>n</sub>.
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;Task

:* &nbsp; show the Bernoulli numbers &nbsp; '''B'''<sub>0</sub> &nbsp; through &nbsp; '''B'''<sub>60</sub>.
:* &nbsp; suppress the output of values which are equal to zero. &nbsp; (Other than &nbsp; '''B'''<sub>1</sub>&nbsp;, all ''odd''  Bernoulli numbers have a value of zero.)
:* &nbsp; express the Bernoulli numbers as fractions &nbsp;(most are improper fractions).
:* &nbsp; the fractions should be reduced.
:* &nbsp; index each number in some way so that it can be discerned which Bernoulli number is being displayed.
:* &nbsp; align the solidi &nbsp; (<big><b>/</b></big>) &nbsp; if used (extra credit).


;An algorithm
The Akiyama–Tanigawa algorithm for the "second Bernoulli numbers" as taken from [[wp:Bernoulli_number#Algorithmic_description|wikipedia]] is as follows:

  '''for''' ''m'' '''from''' 0 '''by''' 1 '''to''' ''n'' '''do'''
     ''A''[''m''] ← 1/(''m''+1)
     '''for''' ''j'' '''from''' ''m'' '''by''' -1 '''to''' 1 '''do'''
       ''A''[''j''-1] ← ''j''×(''A''[''j''-1] - ''A''[''j''])
   '''return''' ''A''[0] (which is ''B''<sub>''n''</sub>)

;See also
* Sequence [http://oeis.org/A027641 A027641 Numerator of Bernoulli number B_n] on The On-Line Encyclopedia of Integer Sequences.
* Sequence [http://oeis.org/A027642 A027642 Denominator of Bernoulli number B_n] on The On-Line Encyclopedia of Integer Sequences.
* Entry [http://mathworld.wolfram.com/BernoulliNumber.html Bernoulli number] on The Eric Weisstein's World of Mathematics (TM).
* Luschny's [http://luschny.de/math/zeta/The-Bernoulli-Manifesto.html The Bernoulli Manifesto] for a discussion on &nbsp; <big> '''B<sub>1</sub> &nbsp; = &nbsp; -&frac12;''' &nbsp; versus &nbsp; '''+&frac12;'''. </big>
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