A174039 A triangle sequence of the form:q=2:t(n,m,q)=Sum[q^i*Floor[Eulerian[n + 1, m]/2^i], {i, 0, 10}]

1, 1, 1, 1, 12, 1, 1, 37, 37, 1, 1, 116, 452, 116, 1, 1, 305, 2544, 2544, 305, 1, 1, 752, 12497, 25552, 12497, 752, 1, 1, 1761, 46541, 171269, 171269, 46541, 1761, 1, 1, 4064, 160080, 969956, 1717376, 969956, 160080, 4064, 1, 1, 9181, 524928, 5006448

Offset

0,5

Comments

Row sums are:

{1, 2, 14, 76, 686, 5700, 52052, 439144, 3985578, 39906884, 439073132,...}.

Links

Table of n, a(n) for n=0..48.

Formula

q=32:

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

Example

{1},
{1, 1},
{1, 12, 1},
{1, 37, 37, 1},
{1, 116, 452, 116, 1},
{1, 305, 2544, 2544, 305, 1},
{1, 752, 12497, 25552, 12497, 752, 1},
{1, 1761, 46541, 171269, 171269, 46541, 1761, 1},
{1, 4064, 160080, 969956, 1717376, 969956, 160080, 4064, 1},
{1, 9181, 524928, 5006448, 14412884, 14412884, 5006448, 524928, 9181, 1},
{1, 20444, 1678653, 24236928, 107117828, 172965424, 107117828, 24236928, 1678653, 20444, 1}

Mathematica

<< DiscreteMath`Combinatorica`
t[n_, m_, q_] = Sum[q^i*Floor[Eulerian[n + 1, m]/2^i], {i, 0, 10}];
Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 1, 10}]

Crossrefs

Sequence in context: A166343 A186432 A176489 * A174148 A155495 A157273

Adjacent sequences: A174036 A174037 A174038 * A174040 A174041 A174042

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Mar 06 2010

Status

approved