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 On 10/20/2014 08:37 AM, Ralf Hemmecke wrote: which gives excellent results. Pari uses $|B_n| = \frac{2n!}{(2\pi)^n}\zeta(n)$ with floats but you have to completely control the precision.  I don't know exactly, but I'd bet that Sage builds on flint2 for the computation of Bernoulli (implemented (if I am not wrong) by Fredrik http://fredrikj.net/). http://flintlib.org/benchmarks.html Since that is free software, it would make sense to think about using that library. Ralf  A little off topic; but I have developed an alternate way of dealing with polynomial sequences like Bernoulli polynomials that are generated by generating functions.  It involves casting the sequences in matrices and apply Pascal Matrices and Umbral calculus.  It makes some known relations obvious and casts a different viewpoint on others.  It might allow some kind of Polynomial sequence algebra or some such.  It does have the advantage of automatically converting some (actually  most) sequences to others by symbolic/parametrized methods. If anybody is interested let me know and I will write up the application to Bernoulli polynomials as a special case. Ray -- The primary use of conversation is to satisfy the impulse to talk George Santanyana