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%I #11 Aug 02 2015 21:40:55
%S 1,1,2,1,12,6,1,42,108,24,1,120,900,960,120,1,310,5400,15600,9000,720,
%T 1,756,27090,168000,252000,90720,5040,1,1778,121716,1428840,4410000,
%U 4021920,987840,40320,1,4080,508200,10442880,58388400,106686720
%N Triangle a(n,k) = k!*C(n-1,k-1)*Stirling_2(n,k), 1<=k<=n.
%e The 3rd row is formed from [ 1,2,6,24 ]*[ 1,3,3,1 ]*[ 1,7,6,1 ] => [ 1,42,108,24 ].
%e 1;
%e 1,2;
%e 1,12,6;
%e 1,42,108,24;
%e 1,120,900,960,120;
%p A048743 := proc(n,k) k!*binomial(n-1,k-1)*combinat[stirling2](n,k) ; end proc:
%p seq(seq(A048743(n,k),k=1..n),n=1..12) ; # _R. J. Mathar_, Aug 30 2011
%t Flatten[Table[k!Binomial[n-1,k-1]StirlingS2[n,k],{n,10},{k,n}]] (* _Harvey P. Dale_, Feb 21 2013 *)
%Y Cf. A007318, A008277. Row sums give A045531.
%K easy,nonn,tabl
%O 1,3
%A _Alford Arnold_
%E More terms from _James A. Sellers_, Apr 22 2000