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Fungrim entry: 30652c

(n)k=(n+k−1)!(n−1)!\left(n\right)_{k} = \frac{\left(n + k - 1\right)!}{\left(n - 1\right)!}
Assumptions:n∈Z≥1  and⁡  k∈Z≥0n \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; k \in \mathbb{Z}_{\ge 0}
TeX:
\left(n\right)_{k} = \frac{\left(n + k - 1\right)!}{\left(n - 1\right)!}

n \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; k \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
RisingFactorial(z)k\left(z\right)_{k} Rising factorial
Factorialn!n ! Factorial
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("30652c"),
    Formula(Equal(RisingFactorial(n, k), Div(Factorial(Sub(Add(n, k), 1)), Factorial(Sub(n, 1))))),
    Variables(n, k),
    Assumptions(And(Element(n, ZZGreaterEqual(1)), Element(k, ZZGreaterEqual(0)))))

Topics using this entry

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2021-03-15 19:12:00.328586 UTC