The factorial n! for non-negative small integer n.

The number of permutations of n distinct objects taken k at a time.

The binomial coefficient n choose r.

Given a sequence Q = [r_1, ..., r_k] of positive integers such that n = r_1 + ... + r_k, return the multinomial coefficient n choose r_1, ..., r_k.

Given an integer n, this function returns the n-th Fibonacci number F_n, which can be defined via the recursion F_0=0, F_1=1 and F_n=F_(n - 1) + F_(n - 2). Note that n is allowed to be negative, and that F_n=( - 1)^(n - 1)F_(-n).

The Stirling number of the first type, [(m atop n)], where m and n are non-negative integers.

The Stirling number of the second type, {(m atop n)}, where m and n are non-negative integers.

The number E(n, r) of permutations p of {1, ..., n} having exactly k ascents (i.e., places where p_i < p_(i + 1))

The nth harmonic number H_n = Sigma_(i=1)^n (1/i).

Returns the nth Bernoulli number B_n as a rational number.

Returns a real approximation to the nth Bernoulli number B_n.

The nth Bernoulli polynomial B_n(x) = sum_(k=0)^n (n choose k) B_k x^(n - k) where B_n is the nth Bernoulli number.