Factorial form of the centred binomial

(2n)!/((n+x)!(n-x)! 2^(2n)), cross-checked against the C(2n, n+x)/2^(2n) form.

Usage

BinomCtrF(x, n)

Arguments

x

deviation from n Heads; zero outside abs(x) <= n.

n

half the number of flips, >= 0.

Value

list(probability).

References

Morin, D. J. (2016). Probability: For the Enthusiastic Beginner. Createspace. Eq (5.5).

Examples

BinomCtrF(1, 10)$probability
#> [1] 0.1601791