cp's OEIS Frontend

A048743 Triangle a(n,k) = k!*C(n-1,k-1)*Stirling_2(n,k), 1<=k<=n.

%I A048743 #12 Jul 02 2025 16:01:57
%S A048743 1,1,2,1,12,6,1,42,108,24,1,120,900,960,120,1,310,5400,15600,9000,720,
%T A048743 1,756,27090,168000,252000,90720,5040,1,1778,121716,1428840,4410000,
%U A048743 4021920,987840,40320,1,4080,508200,10442880,58388400,106686720
%N A048743 Triangle a(n,k) = k!*C(n-1,k-1)*Stirling_2(n,k), 1<=k<=n.
%e A048743 The 3rd row is formed from [ 1,2,6,24 ]*[ 1,3,3,1 ]*[ 1,7,6,1 ] => [ 1,42,108,24 ].
%e A048743 1;
%e A048743 1,2;
%e A048743 1,12,6;
%e A048743 1,42,108,24;
%e A048743 1,120,900,960,120;
%p A048743 A048743 := proc(n,k) k!*binomial(n-1,k-1)*combinat[stirling2](n,k) ; end proc:
%p A048743 seq(seq(A048743(n,k),k=1..n),n=1..12) ; # _R. J. Mathar_, Aug 30 2011
%t A048743 Flatten[Table[k!Binomial[n-1,k-1]StirlingS2[n,k],{n,10},{k,n}]] (* _Harvey P. Dale_, Feb 21 2013 *)
%Y A048743 Cf. A007318, A008277. Row sums give A045531.
%K A048743 easy,nonn,tabl
%O A048743 1,3
%A A048743 _Alford Arnold_
%E A048743 More terms from _James Sellers_, Apr 22 2000