%I A153274
%S A153274 2,6,15,24,105,280,120,945,3640,9945,720,10395,58240,208845,576576,5040,
%T A153274 135135,1106560,5221125,17873856,49579075,40320,2027025,24344320,
%U A153274 151412625,643458816,2131900225,5925744000,362880,34459425,608608000
%N A153274 A Pochhammer function-based triangular sequence: w(n,m,j)=m^(n + 1)*Pochhammer[j/
               m,n+1]; t(n,m)=sum_coefficients(w(n,m,j) in j).
%C A153274 Row sums are:
%C A153274 {2, 21, 409, 14650, 854776, 73920791, 8878927331, 1413788600036,
%C A153274 288152651134776, 73152069870215127}.
%C A153274 The first column is the factorials starting at 2.
%F A153274 w(n,m,j)=m^(n + 1)*Pochmammer[j/m,n+1]; w(n,m,j)=Product[m*k + j, {k, 
               0, n}]; t(n,m)=sum_coefficients(w(n,m,j) in j).
%e A153274 {2},
%e A153274 {6, 15},
%e A153274 {24, 105, 280},
%e A153274 {120, 945, 3640, 9945},
%e A153274 {720, 10395, 58240, 208845, 576576},
%e A153274 {5040, 135135, 1106560, 5221125, 17873856, 49579075},
%e A153274 {40320, 2027025, 24344320, 151412625, 643458816, 2131900225, 5925744000},
%e A153274 {362880, 34459425, 608608000, 4996616625, 26381811456, 104463111025, 
               337767408000, 939536222625},
%e A153274 {3628800, 654729075, 17041024000, 184874815125, 1213563326976, 5745471106375, 
               21617114112000, 68586144251625, 190787784140800},
%e A153274 {39916800, 13749310575, 528271744000, 7579867420125, 61891729675776, 
               350473737488875, 1534815101952000, 5555477684381625, 17361688356812800, 
               48279601331512551}
%t A153274 Clear[t, n, m, j, k];
%t A153274 t[n_, m_] = Product[m*k + j, {k, 0, n}]
%t A153274 Table[Table[Apply[Plus, CoefficientList[t[n, m], j]], {m, 1, n}], {n, 
               1, 10}];
%t A153274 Flatten[%]
%Y A153274 Sequence in context: A090979 A050508 A033298 this_sequence A091766 A138621 
               A163061
%Y A153274 Adjacent sequences: A153271 A153272 A153273 this_sequence A153275 A153276 
               A153277
%K A153274 nonn,uned,tabl
%O A153274 0,1
%A A153274 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Dec 22 2008