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%I #24 Oct 24 2024 15:53:00
%S 1,1,1,1,2,8,1,3,18,162,1,4,32,384,6144,1,5,50,750,15000,375000,1,6,
%T 72,1296,31104,933120,33592320,1,7,98,2058,57624,2016840,84707280,
%U 4150656720,1,8,128,3072,98304,3932160,188743680,10569646080,676457349120
%N Triangle read by rows: T(n,k) = n^k * k!.
%F T(n,k) = Product_{j=1..n} n*j.
%e Triangle T(n,k) begins:
%e 1;
%e 1, 1;
%e 1, 2, 8;
%e 1, 3, 18, 162;
%e 1, 4, 32, 384, 6144;
%e 1, 5, 50, 750, 15000, 375000;
%e 1, 6, 72, 1296, 31104, 933120, 33592320;
%e 1, 7, 98, 2058, 57624, 2016840, 84707280, 4150656720;
%e ...
%t t[n_, m_] =Product[m*k, {k, 1, n}];
%t Table[Table[t[n, m], {n, 1, m}], {m, 1, 10}];
%t Flatten[%]
%Y Main diagonal gives A061711.
%Y Row sums give A368561.
%Y Cf. A000165, A008544.
%K nonn,tabl
%O 0,5
%A _Roger L. Bagula_, Dec 20 2008
%E Formula corrected by _Georg Fischer_, Oct 24 2024