Re: Bernoulli Numbers

*To*: mathgroup at smc.vnet.net*Subject*: [mg122624] Re: Bernoulli Numbers*From*: Bob Hanlon <hanlonr357 at gmail.com>*Date*: Thu, 3 Nov 2011 03:48:50 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <201111021122.GAA03586@smc.vnet.net>

Clear[b]; b[0] = 1; b[n_Integer?Positive] := b[n] = (x /. Solve[ Sum[Binomial[n + 1, k]*b[k], {k, 0, n - 1}] + (n + 1)*x == 0, x][[1]]) And @@ Table[b[n] == BernoulliB[n], {n, 0, 20}] True Sum[Binomial[21, k]*b[k], {k, 0, 20}] == 0 True Table[{n, b[n]}, {n, 0, 20}] // Grid Bob Hanlon On Wed, Nov 2, 2011 at 7:22 AM, David Turner <DTurner at faulkner.edu> wrote: > 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

**References**:**Bernoulli Numbers***From:*David Turner <DTurner@faulkner.edu>