bernoulli.md

On Rosetta Code, the list of Tasks uncompleted in R contains the following challenge: print the Bernoulli numbers from B0 to B60. After seeing some solutions, including one in in Python , I wanted to try in R. There are examples of code on that website, and a nice description of the algorithm here.

    library(MASS)
    library(pander)

    n <- 20L
    js <- 0:n
    Bs <- lapply((n+1):1,function(x) numeric(x))
    Bs[[1]] <- 1/(js+1)
    for(i in 2:length(Bs)){
      Bs[[i]] <- seq_along(Bs[[i]])*(Bs[[i-1]][-length(Bs[[i-1]])] - Bs[[i-1]][-1])
    }

    Bn <- sapply(Bs,"[",1)

    pander(cbind(js,zapsmall(Bn)))

Bn	value
0	1.000
1	0.500
2	0.167
3	0.000
4	-0.033
5	0.000
6	0.024
7	0.000
8	-0.033
9	0.000
10	0.076
11	0.000
12	-0.253
13	0.000
14	1.167
15	0.001
16	-7.069
17	0.641
18	69.997
19	323.014
20	5986.642

The value of every odd bernoulli number > 3 should be 0. But, I start getting nonzero values after 15