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A153273 Triangle read by rows: T(n,k) = Product_{i=0..k-2} (i*n + n - 1).

%I A153273 #11 Sep 08 2022 08:45:39
%S A153273 1,2,10,3,21,231,4,36,504,9576,5,55,935,21505,623645,6,78,1560,42120,
%T A153273 1432080,58715280,7,105,2415,74865,2919735,137227545,7547514975,8,136,
%U A153273 3536,123760,5445440,288608320,17893715840,1270453824640,9,171,4959,193401,9476649,559122291,38579438079,3047775608241,271252029133449
%N A153273 Triangle read by rows: T(n,k) = Product_{i=0..k-2} (i*n + n - 1).
%C A153273 Row sums are {1, 12, 255, 10120, 646145, 60191124, 7687739647, 1288641721680, 274338952977249, 72299818200530140, ...}.
%C A153273 A153187 without its diagonal. - _R. J. Mathar_, Sep 04 2016
%H A153273 G. C. Greubel, <a href="/A153273/b153273.txt">Rows n = 2..100 of triangle, flattened</a>
%e A153273 Triangle begins as:
%e A153273   1;
%e A153273   2,  10;
%e A153273   3,  21,  231;
%e A153273   4,  36,  504,   9576;
%e A153273   5,  55,  935,  21505,  623645;
%e A153273   6,  78, 1560,  42120, 1432080,  58715280;
%e A153273   7, 105, 2415,  74865, 2919735, 137227545,  7547514975;
%e A153273   8, 136, 3536, 123760, 5445440, 288608320, 17893715840, 1270453824640;
%p A153273 A153273 := proc(n,m)
%p A153273     local i;
%p A153273     mul( n-1+i*n, i=0..m-2) ;
%p A153273 end proc:
%p A153273 seq(seq( A153273(n,m), m=2..n), n=2..12) ; # _R. J. Mathar_, Sep 04 2016
%t A153273 Table[n^(k-1)*Pochhammer[(n-1)/n, k-1], {n,2,12}, {k,2,n}]//Flatten (* modified by _G. C. Greubel_, Mar 05 2020 *)
%o A153273 (PARI) T(n,k) = prod(j=0, k-2, j*n+n-1);
%o A153273 for(n=2,12, for(k=2,n, print1(T(n,k), ", "))) \\ _G. C. Greubel_, Mar 05 2020
%o A153273 (Magma) [(&*[j*n+n-1: j in [0..k-2]]): k in [2..n], n in [2..12]]; // _G. C. Greubel_, Mar 05 2020
%o A153273 (Sage) [[n^(k-1)*rising_factorial((n-1)/n, k-1) for k in (2..n)] for n in (2..12)] # _G. C. Greubel_, Mar 05 2020
%o A153273 (GAP) Flat(List([2..12], n-> List([2..n], k-> Product([0..k-2], j-> (j+1)*n-1) ))); # _G. C. Greubel_, Mar 05 2020
%Y A153273 Cf. A000027, A014105, A033594.
%K A153273 nonn,tabl,easy
%O A153273 2,2
%A A153273 _Roger L. Bagula_, Dec 22 2008
%E A153273 Edited by _G. C. Greubel_, Mar 05 2020