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