%I #2 Mar 30 2012 17:34:39

%S 1,1,1,1,19,1,1,71,71,1,1,281,2064,281,1,1,942,19925,19925,942,1,1,

%T 3000,182094,372304,182094,3000,1,1,9265,708780,2645662,2645662,

%U 708780,9265,1,1,28435,2470768,15065554,26673373,15065554,2470768,28435,1,1,86456

%N A triangle sequence of the form:q=3:t(n,m,q)=Sum[q^i*Floor[Eulerian[n + 1, m]/2^i], {i, 0, 10}]

%C Row sums are:

%C {1, 2, 21, 144, 2628, 41736, 742494, 6727416, 61802889, 620052978, 6825051876,...}.

%F q=3:

%F t(n,m,q)=Sum[q^i*Floor[Eulerian[n + 1, m]/2^i], {i, 0, 10}]

%e {1},

%e {1, 1},

%e {1, 19, 1},

%e {1, 71, 71, 1},

%e {1, 281, 2064, 281, 1},

%e {1, 942, 19925, 19925, 942, 1},

%e {1, 3000, 182094, 372304, 182094, 3000, 1},

%e {1, 9265, 708780, 2645662, 2645662, 708780, 9265, 1},

%e {1, 28435, 2470768, 15065554, 26673373, 15065554, 2470768, 28435, 1}, \ Q{1, 86456, 8121608, 77802257, 224016167, 224016167, 77802257, 8121608, 86456, 1},

%e {1, 261554, 26090712, 376717869, 1665099897, 2688711810, 1665099897, 376717869, 26090712, 261554, 1}

%t << DiscreteMath`Combinatorica`

%t t[n_, m_, q_] = Sum[q^i*Floor[Eulerian[n + 1, m]/2^i], {i, 0, 10}];

%t Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 1, 10}]

%K nonn,tabl,uned

%O 0,5

%A _Roger L. Bagula_, Mar 06 2010