Binomial Coefficients
Compute the Binomial coefficients.
nchoosek(n, k)
n, k |
integers with |
Alias for the corresponding R function choose.
integer, the Binomial coefficient ({n \over k}).
In Matlab/Octave, if n is a vector all combinations of k
elements from vector n will be generated. Here, use the function
combs instead.
S <- sapply(0:6, function(k) nchoosek(6, k)) # 1 6 15 20 15 6 1 # Catalan numbers catalan <- function(n) choose(2*n, n)/(n+1) catalan(0:10) # 1 1 2 5 14 42 132 429 1430 4862 16796 # Relations n <- 10 sum((-1)^c(0:n) * sapply(0:n, function(k) nchoosek(n, k))) # 0
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