A174033 A triangle sequence of the form:t(n,m]=Sum[Floor[Eulerian[n + 1, m]/2^i], {i, 0, 10}]

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

Offset

0,5

Comments

Row Sums are:

{1, 2, 9, 40, 230, 1420, 10052, 80572, 725375, 7254022, 79794578,...}.

Links

Table of n, a(n) for n=0..51.

Formula

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

Example

{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},
{1, 4064, 305120, 4404821, 19466715, 31433136, 19466715, 4404821, 305120, 4064, 1}

Mathematica

Clear[t, n, m, i]
<< 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[%]

Crossrefs

Sequence in context: A176561 A176284 A154233 * A119727 A157272 A176200

Adjacent sequences: A174030 A174031 A174032 * A174034 A174035 A174036

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Mar 06 2010

Status

approved