cp's OEIS Frontend

A174033 T(n, m) = Sum_{i=0..10} floor(Eulerian(n+1, m)/2^i).

%I A174033 #8 Feb 08 2025 01:25:19
%S A174033 1,1,1,1,7,1,1,19,19,1,1,49,130,49,1,1,110,599,599,110,1,1,236,2376,
%T A174033 4826,2376,236,1,1,487,8578,31220,31220,8578,487,1,1,997,29200,176378,
%U A174033 312223,176378,29200,997,1,1,2018,95630,909937,2619425,2619425,909937,95630,2018,1
%N A174033 T(n, m) = Sum_{i=0..10} floor(Eulerian(n+1, m)/2^i).
%F A174033 T(n, m) = Sum_{i=0..10} floor(Eulerian(n+1, m)/2^i), where Eulerian(n, k) = A008292(n, k).
%e A174033 Triangle begins:
%e A174033   {1},
%e A174033   {1, 1},
%e A174033   {1, 7, 1},
%e A174033   {1, 19, 19, 1},
%e A174033   {1, 49, 130, 49, 1},
%e A174033   {1, 110, 599, 599, 110, 1},
%e A174033   {1, 236, 2376, 4826, 2376, 236, 1},
%e A174033   {1, 487, 8578, 31220, 31220, 8578, 487, 1},
%e A174033   {1, 997, 29200, 176378, 312223, 176378, 29200, 997, 1},
%e A174033   {1, 2018, 95630, 909937, 2619425, 2619425, 909937, 95630, 2018, 1},
%e A174033   ...
%t A174033 << DiscreteMath`Combinatorica`
%t A174033 Sum[Floor[Eulerian[n + 1, m]/2^i], {i, 0, 10}];
%t A174033 Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
%t A174033 Flatten[%]
%Y A174033 Cf. A008292, A176200.
%K A174033 nonn,tabl,uned,less
%O A174033 0,5
%A A174033 _Roger L. Bagula_, Mar 06 2010