: Mathematics: Fuss-Catalan number

mathematical analysis > combinatorics > permutation > Fuss-Catalan number

algebra > combinatorics > permutation > Fuss-Catalan number

... > calculus > sequence > integer sequence > binomial coefficient > Fuss-Catalan number

mathematical analysis > combinatorics > binomial coefficient > Fuss-Catalan number

algebra > combinatorics > binomial coefficient > Fuss-Catalan number

Fuss-Catalan number

In combinatorial mathematics and statistics, the Fuss–Catalan numbers are numbers of the form
${\\displaystyle A_{m}(p,r)\\equiv {\ rac {r}{mp+r}}{\inom {mp+r}{m}}={\ rac {r}{m!}}\\prod _{i=1}^{m-1}(mp+r-i)=r{\ rac {\\Gamma (mp+r)}{\\Gamma (1+m)\\Gamma (m(p-1)+r+1)}}.}$
They are named after N. I. Fuss and Eugène Charles Catalan. In some publications this equation is sometimes referred to as Two-parameter Fuss–Catalan numbers or Raney numbers. The implication is the single-parameter Fuss-Catalan numbers are when ${\\displaystyle \\,r=1\\,}$ and ${\\displaystyle \\,p=2\\,}$ .
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Fuss%E2%80%93Catalan_number)

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