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%I #2 Mar 30 2012 17:34:39
%S 1,1,1,1,-23,1,1,-259,-259,1,1,-1999,-5199,-1999,1,1,-13551,-72841,
%T -72841,-13551,1,1,-86631,-866319,-1758119,-866319,-86631,1,1,-537755,
%U -9382311,-34140947,-34140947,-9382311,-537755,1,1,-3286559,-95821919
%N A symmetrical triangle sequence:q=3:t(n,m,q)=(1 - q^n)*Eulerian[n + 1, m] - (1 - q^n) + 1
%C Row sums are:
%C {1, 2, -21, -516, -9195, -172782, -3664017, -88122024, -2380433751,
%C -71421844770, -2357006556861,...}.
%F q=3:t(n,m,q)=(1 - q^n)*Eulerian[n + 1, m] - (1 - q^n) + 1
%e {1},
%e {1, 1},
%e {1, -23, 1},
%e {1, -259, -259, 1},
%e {1, -1999, -5199, -1999, 1},
%e {1, -13551, -72841, -72841, -13551, 1},
%e {1, -86631, -866319, -1758119, -866319, -86631, 1},
%e {1, -537755, -9382311, -34140947, -34140947, -9382311, -537755, 1},
%e {1, -3286559, -95821919, -578808479, -1024599839, -578808479, -95821919, -3286559, 1},
%e {1, -19918183, -941567197, -8959069261, -25790367745, -25790367745, -8959069261, -941567197, -19918183, 1},
%e {1, -120162679, -9012850527, -130111500375, -575016096423, -928485336855, -575016096423, -130111500375, -9012850527, -120162679, 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
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