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.
The factorial n! for positive small integer n.
Tests if n = k! for some k. If so, return true and k, false otherwise.
The unrestricted partitions of the positive integer n.
This function returns a sequence of integer sequences, each
of which is a different sequence of positive integers (in descending
order) adding up to n.
The integer n must be small.
The number of unrestricted partitions of the non-negative integer n.
The integer n must be small.
The partitions of the positive integer n, restricted to
elements of the positive integer sequence M.
The partitions of the positive integer n into k parts, restricted to
elements of the positive integer sequence M.
The Stirling number of the first type, s(n, k),
where n and k are non-negative integers.
The Stirling number of the second type, S(n,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).
Given an integer n, this function returns the n-th Fibonacci
number Fn, which can be defined via the recursion F0 = 0, F1 = 1
and 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 an integer n, this function returns the n-th Lucas number
Ln, which can be defined via the recursion L0 = 2, L1 = 1
and 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 and 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.
V2.28, 13 July 2023