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${}\pochhammer{a}{0}:=1\quad\textrm{%
and}\quad\pochhammer{a}{k}:=\prod_{n=1}^{k}(a+n-1),\quad k=1,2,3,\ldots}}$

$\pochhammer{1}{n}=n!}}$

Constraint(s): $n=0,1,2,\ldots}}$

${}\binomial{\alpha}{\beta}:=\frac{%
\Gamma\left(\alpha+1\right)}{\Gamma\left(\beta+1\right)\Gamma\left(\alpha-%
\beta+1\right)}}}$

$\binomial{\alpha}{k}:=\frac{%
\pochhammer{-\alpha}{k}}{k!}(-1)^{k}}}$

Constraint(s): $k=0,1,2,\ldots}}$

$\binomial{n}{k}:=\frac{n!}{k!\,(n-k)% !},\quad k=0,1,2,\ldots,n}}$

Constraint(s): $n=0,1,2,\ldots}}$

$\binomial{2n}{n}=\frac{\pochhammer{% \frac{1}{2}}{n}}{n!}4^{n}}}$

Constraint(s): $n=0,1,2,\ldots}}$