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

1, 1, 1, 1, 7, 1, 1, 19, 19, 1, 1, 49, 130, 49, 1, 1, 110, 599, 599, 110, 1, 1, 236, 2376, 4826, 2376, 236, 1, 1, 487, 8578, 31220, 31220, 8578, 487, 1, 1, 997, 29200, 176378, 312223, 176378, 29200, 997, 1, 1, 2018, 95630, 909937, 2619425, 2619425, 909937, 95630, 2018, 1

Offset: 0

Author

Roger L. Bagula, Mar 06 2010

Keywords

• nonn
• tabl
• uned
• less

Examples

			Triangle begins:
  {1},
  {1, 1},
  {1, 7, 1},
  {1, 19, 19, 1},
  {1, 49, 130, 49, 1},
  {1, 110, 599, 599, 110, 1},
  {1, 236, 2376, 4826, 2376, 236, 1},
  {1, 487, 8578, 31220, 31220, 8578, 487, 1},
  {1, 997, 29200, 176378, 312223, 176378, 29200, 997, 1},
  {1, 2018, 95630, 909937, 2619425, 2619425, 909937, 95630, 2018, 1},
  ...
		

Crossrefs

Cf. A008292, A176200.

Programs

Mathematica

<< DiscreteMath`Combinatorica`
Sum[Floor[Eulerian[n + 1, m]/2^i], {i, 0, 10}];
Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]

Formula

T(n, m) = Sum_{i=0..10} floor(Eulerian(n+1, m)/2^i), where Eulerian(n, k) = A008292(n, k).