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A174033 A triangle sequence of the form:t(n,m]=Sum[Floor[Eulerian[n + 1, m]/2^i], {i, 0, 10}] 0
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified May 25 07:56 EDT 2020. Contains 334585 sequences. (Running on oeis4.)