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%I #4 Dec 26 2023 16:39:56
%S 1,1,1,1,-44,1,1,-629,-629,1,1,-6374,-16574,-6374,1,1,-57287,-307922,
%T -307922,-57287,1,1,-487304,-4873049,-9889424,-4873049,-487304,1,1,
%U -4030217,-70315835,-255869693,-255869693,-70315835,-4030217,1,1
%N A symmetrical triangle sequence:q=4:t(n,m,q)=(1 - q^n)*Eulerian[n + 1, m] - (1 - q^n) + 1.
%C Row sums are:
%C {1, 2, -42, -1256, -29320, -730416, -20610128, -660431488, -23780750976,
%C -951261896960, -41855747025664,...}.
%F q=4:t(n,m,q)=(1 - q^n)*Eulerian[n + 1, m] - (1 - q^n) + 1.
%e {1},
%e {1, 1},
%e {1, -44, 1},
%e {1, -629, -629, 1},
%e {1, -6374, -16574, -6374, 1},
%e {1, -57287, -307922, -307922, -57287, 1},
%e {1, -487304, -4873049, -9889424, -4873049, -487304, 1},
%e {1, -4030217, -70315835, -255869693, -255869693, -70315835, -4030217, 1},
%e {1, -32833034, -957269744, -5782349654, -10235846114, -5782349654, -957269744, -32833034, 1},
%e {1, -265288715, -12540658976, -119325134312, -343499866478, -343499866478, -119325134312, -12540658976, -265288715, 1},
%e {1, -2133850124, -160050293699, -2310521381024, -10211141838974, -16488052298024, -10211141838974, -2310521381024, -160050293699, -2133850124, 1}
%t << DiscreteMath`Combinatorica`
%t t[n_, m_, q_] = (1 - q^n)*Eulerian[n + 1, m] - (1 - q^n) + 1;
%t Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 2, 12}]
%K sign,tabl,uned
%O 0,5
%A _Roger L. Bagula_, Mar 28 2010