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Re: Bernoulli Numbers

  • To: mathgroup at smc.vnet.net
  • Subject: [mg122600] Re: Bernoulli Numbers
  • From: "Dr. Wolfgang Hintze" <weh at snafu.de>
  • Date: Thu, 3 Nov 2011 03:44:09 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <j8r9gv$3jd$1@smc.vnet.net>

Why not solve by hand for b[n] (and preferrably use lower case symbols 
for your own ones), i.e.

b[n_] := -Sum[Binomial[n + 1, k]*b[k], {k, 0, n - 1}]/(n + 1)

and then calculate the values recursively in a table
b[0] = 1;

Table[{n, b[n]}, {n, 0, 16}]

{{0, 1}, {1, -(1/2)}, {2, 1/6}, {3, 0}, {4, -(1/30)},
{5, 0}, {6, 1/42}, {7, 0}, {8, -(1/30)}, {9, 0},
{10, 5/66}, {11, 0}, {12, -(691/2730)}, {13, 0},
{14, 7/6}, {15, 0}, {16, -(3617/510)}}

Regards,
Wolfgang

"David Turner" <DTurner at faulkner.edu> schrieb im Newsbeitrag 
news:j8r9gv$3jd$1 at smc.vnet.net...
> Hello,
>
> I wish to compute several Bernoulli numbers, say B0 through B20.  The 
> Bernoulli numbers are defined recursively by
>
> B0 = 1, and Solve[Sum[Binomial[n,k]*Bk,{k,0,n-1}]==0,Bn-1] for n > 1
>
> I am trying to compute these numbers in some type of loop, and 
> display them in a table.  Any help is greatly appreciated.
>
> Thanks,
>
> David
>
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