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 > > _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ > _ _ _ > > This email and any files transmitted with it are confidential and > intended solely for the use of the individual or entity to whom they > are addressed. This message contains confidential information and is > intended only for the individual named. If you are not the named > addressee you should not dissem inate, distribute or copy this > e-mail. Please notify the sender immediately by e-mail if you have > received this e-mail by mistake and delete this e-mail from your > system. If you are not the intended recipient you are notified that > disclosing, copying, distributing or taking any action in reliance on > the contents of this information is strictly prohibited.

**Follow-Ups**:**Re: Bernoulli Numbers***From:*DrMajorBob <btreat1@austin.rr.com>