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It seems, according to Sloane, that the formula should read

${\displaystyle N(n,k)={\frac {1}{k}}{n \choose {k-1}}{n-1 \choose k-1}}$

ManiacParisien ( talk) 12:40, 4 December 2013 (UTC) reply

That's the same, just written differently. Both expressions evaluate to

${\displaystyle N(n,k)={\frac {n!(n-1)!}{k!(k-1)!(n-k+1)!(n-k)!}}\;.}$

MuDavid ( talk) 08:12, 9 May 2017 (UTC) reply