A176428 - OEIS

%I #2 Mar 30 2012 17:34:40

%S 1,1,1,1,4,1,1,15,15,1,1,54,194,54,1,1,185,2118,2118,185,1,1,608,

%T 20831,65344,20831,608,1,1,1939,194633,1835923,1835923,194633,1939,1,

%U 1,6058,1777912,50102326,151670254,50102326,1777912,6058,1,1,18669,16091400

%N A symmetrical triangle sequence:q=3;c(n,q)=Product[1 - q^i, {i, 1, n}];t(n,m,q)=-Eulerian[n + 1, m] + 2*c(n, q)/(c(m, q)*c(n - m, q))

%C Row sums are:

%C {1, 2, 6, 32, 304, 4608, 108224, 4064992, 255442848, 27438829376, 5089613338048,...}.

%F q=3;

%F c(n,q)=Product[1 - q^i, {i, 1, n}];

%F t(n,m,q)=-Eulerian[n + 1, m] + 2*c(n, q)/(c(m, q)*c(n - m, q))

%e {1},

%e {1, 1},

%e {1, 4, 1},

%e {1, 15, 15, 1},

%e {1, 54, 194, 54, 1},

%e {1, 185, 2118, 2118, 185, 1},

%e {1, 608, 20831, 65344, 20831, 608, 1},

%e {1, 1939, 194633, 1835923, 1835923, 194633, 1939, 1},

%e {1, 6058, 1777912, 50102326, 151670254, 50102326, 1777912, 6058, 1},

%e {1, 18669, 16091400, 1356482448, 12346822170, 12346822170, 1356482448, 16091400, 18669, 1},

%e {1, 57012, 145120205, 36651252032, 1001545933970, 3012928611608, 1001545933970, 36651252032, 145120205, 57012, 1}

%t << DiscreteMath`Combinatorica` ;

%t c[n_, q_] = Product[1 - q^i, {i, 1, n}];

%t t[n_, m_, q_] = -Eulerian[n + 1, m] + 2*c[n, q]/(c[m, q]*c[n - m, q]);

%t Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 2, 12}]

%K nonn,tabl,uned

%O 0,5

%A _Roger L. Bagula_, Apr 17 2010