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Triangle read by rows: T(n,k) = (n-1)!*n^(k-1)*binomial(n,k)/(k-1)!.
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%I #9 Apr 09 2023 13:59:26

%S 1,2,2,6,18,9,24,144,192,64,120,1200,3000,2500,625,720,10800,43200,

%T 64800,38880,7776,5040,105840,617400,1440600,1512630,705894,117649

%N Triangle read by rows: T(n,k) = (n-1)!*n^(k-1)*binomial(n,k)/(k-1)!.

%H I. Mezo, A. Baricz, <a href="http://arxiv.org/abs/1408.3999">On the generalization of the Lambert W function with applications in theoretical physics</a>, arXiv preprint arXiv:1408.3999, 2014

%t Table[(n-1)! n^(k-1) Binomial[n,k]/(k-1)!,{n,10},{k,n}]//Flatten (* _Harvey P. Dale_, Apr 09 2023 *)

%Y Row sums = A052885.

%K nonn,tabl

%O 1,2

%A _N. J. A. Sloane_, Mar 26 2015