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 = [r1, ..., rk] of positive integers
such that n = r1 + ... + rk, return the multinomial
coefficient n choose r1, ..., rk.
Given an integer n, this function returns the n-th Fibonacci
number Fn, which can be defined via the recursion F0 = 0, F1 = 1,
Fn = Fn - 1 + Fn - 2 for all integers n. Note that n is
allowed to be negative, and that F - n = ( - 1)n + 1 Fn.
Given a small non-negative integer n, this function returns the
n-th Catalan number Cn, defined via the recursion
C0 = 1, Cn + 1 = Cn.(4n + 2)/(n + 2).
Given an integer n, this function returns the n-th Lucas number
Ln, which can be defined via the recursion L0 = 2, L1 = 1,
Ln = Ln - 1 + Ln - 2 for all integers n. Note that n is
allowed to be negative, and that L - n = ( - 1)nLn.
The nth member of the generalized Fibonacci sequence defined by
G0 = g0, G1 = g1, Gn = Gn - 1 + Gn - 2 for all integers
n. Note that n is allowed to be negative. The Fibonacci and Lucas
numbers are special cases where (g0, g1) = (0, 1) or (2, 1)
respectively.
The Stirling number of the first type, [(n atop k)],
where n and k are non-negative integers.
The Stirling number of the second type, {(n atop k)},
where n and k are non-negative integers.
The nth Bell number, giving the number of partitions of a set of size n.
(Not to be confused with NumberOfPartitions(n), which gives the number
of partitions of the integer n.)
This is equal to the sum of StirlingSecond(n,k) for k between 0
and n (inclusive).
The number E(n, r) of permutations p of {1, ..., n} having exactly
r ascents (i.e., places where pi < pi + 1)
The nth harmonic number Hn = Σi=1n (1/i).
Returns the nth Bernoulli number Bn as a rational number.
Returns a real approximation to the nth Bernoulli number Bn.
The nth Bernoulli polynomial
Bn(x) = ∑k=0n (n choose k) Bk xn - k where Bn is the nth
Bernoulli number.
V2.28, 13 July 2023