combinat-0.2.4.1: Generation of various combinatorial objects.Source codeContentsIndex
Math.Combinat.Numbers
Contents
Catalan numbers
Stirling numbers
Bernoulli numbers
Description

A few important number sequences.

See the "On-Line Encyclopedia of Integer Sequences", http://www.research.att.com/~njas/sequences/ .

Synopsis
paritySign :: Integral a => a -> Integer
factorial :: Integral a => a -> Integer
doubleFactorial :: Integral a => a -> Integer
binomial :: Integral a => a -> a -> Integer
pascalRow :: Integral a => a -> [Integer]
multinomial :: Integral a => [a] -> Integer
catalan :: Integral a => a -> Integer
catalanTriangle :: Integral a => a -> a -> Integer
signedStirling1stArray :: Integral a => a -> Array Int Integer
signedStirling1st :: Integral a => a -> a -> Integer
unsignedStirling1st :: Integral a => a -> a -> Integer
stirling2nd :: Integral a => a -> a -> Integer
bernoulli :: Integral a => a -> Rational
Documentation
paritySign :: Integral a => a -> IntegerSource
(-1)^k
factorial :: Integral a => a -> IntegerSource
A000142.
doubleFactorial :: Integral a => a -> IntegerSource
A006882.
binomial :: Integral a => a -> a -> IntegerSource
A007318.
pascalRow :: Integral a => a -> [Integer]Source

A given row of the Pascal triangle; equivalent to a sequence of binomial numbers, but much more efficient. You can also left-fold over it. 

 pascalRow n == [ binomial n k | k<-[0..n] ]
multinomial :: Integral a => [a] -> IntegerSource
Catalan numbers
catalan :: Integral a => a -> IntegerSource
Catalan numbers. OEIS:A000108.
catalanTriangle :: Integral a => a -> a -> IntegerSource

Catalan's triangle. OEIS:A009766. Note: 

 catalanTriangle n n == catalan n
 catalanTriangle n k == countStandardYoungTableaux (toPartition [n,k])
Stirling numbers
signedStirling1stArray :: Integral a => a -> Array Int IntegerSource
Rows of (signed) Stirling numbers of the first kind. OEIS:A008275. Coefficients of the polinomial (x-1)*(x-2)*...*(x-n+1). This function uses the recursion formula.
signedStirling1st :: Integral a => a -> a -> IntegerSource
(Signed) Stirling numbers of the first kind. OEIS:A008275. This function uses signedStirling1stArray, so it shouldn't be used to compute many Stirling numbers.
unsignedStirling1st :: Integral a => a -> a -> IntegerSource
(Unsigned) Stirling numbers of the first kind. See signedStirling1st.
stirling2nd :: Integral a => a -> a -> IntegerSource
Stirling numbers of the second kind. OEIS:A008277. This function uses an explicit formula.
Bernoulli numbers
bernoulli :: Integral a => a -> RationalSource
Bernoulli numbers. bernoulli 1 == -1%2 and bernoulli k == 0 for k>2 and odd. This function uses the formula involving Stirling numbers of the second kind. Numerators: A027641, denominators: A027642.
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