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A174040
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A triangle sequence of the form:q=3:t(n,m,q)=Sum[q^i*Floor[Eulerian[n + 1, m]/2^i], {i, 0, 10}]
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0
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1, 1, 1, 1, 19, 1, 1, 71, 71, 1, 1, 281, 2064, 281, 1, 1, 942, 19925, 19925, 942, 1, 1, 3000, 182094, 372304, 182094, 3000, 1, 1, 9265, 708780, 2645662, 2645662, 708780, 9265, 1, 1, 28435, 2470768, 15065554, 26673373, 15065554, 2470768, 28435, 1, 1, 86456
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OFFSET
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0,5
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COMMENTS
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Row sums are:
{1, 2, 21, 144, 2628, 41736, 742494, 6727416, 61802889, 620052978, 6825051876,...}.
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LINKS
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FORMULA
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q=3:
t(n,m,q)=Sum[q^i*Floor[Eulerian[n + 1, m]/2^i], {i, 0, 10}]
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EXAMPLE
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{1},
{1, 1},
{1, 19, 1},
{1, 71, 71, 1},
{1, 281, 2064, 281, 1},
{1, 942, 19925, 19925, 942, 1},
{1, 3000, 182094, 372304, 182094, 3000, 1},
{1, 9265, 708780, 2645662, 2645662, 708780, 9265, 1},
{1, 28435, 2470768, 15065554, 26673373, 15065554, 2470768, 28435, 1}, \ Q{1, 86456, 8121608, 77802257, 224016167, 224016167, 77802257, 8121608, 86456, 1},
{1, 261554, 26090712, 376717869, 1665099897, 2688711810, 1665099897, 376717869, 26090712, 261554, 1}
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MATHEMATICA
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<< 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}]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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