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A142470
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A new {1,8,1} type symmetrical triangle sequence related to A008459: f(n,m)=Binomial[n, m]*Product[k!*(n + k)!/((m + k)!*(n - m + k)!), {k, 1, 2}]; t(n,m)=2^(m - n)*f(n, m)*Sum[Binomial[n, k]*Binomial[k, m], {k, m, n}].
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0
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1, 1, 1, 1, 8, 1, 1, 30, 30, 1, 1, 80, 300, 80, 1, 1, 175, 1750, 1750, 175, 1, 1, 336, 7350, 19600, 7350, 336, 1, 1, 588, 24696, 144060, 144060, 24696, 588, 1, 1, 960, 70560, 790272, 1728720, 790272, 70560, 960, 1, 1, 1485, 178200, 3492720, 14669424
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| Row sums are:
{1, 2, 10, 62, 462, 3852, 34974, 338690, 3452306, 36683660, 403472368}.
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FORMULA
| A new {1,8,1} type symmetrical triangle sequence related to A008459: f(n,m)=Binomial[n, m]*Product[k!*(n + k)!/((m + k)!*(n - m + k)!), {k, 1, 2}]; t(n,m)=2^(m - n)*f(n, m)*Sum[Binomial[n, k]*Binomial[k, m], {k, m, n}].
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EXAMPLE
| {1},
{1, 1},
{1, 8, 1},
{1, 30, 30, 1},
{1, 80, 300, 80, 1},
{1, 175, 1750, 1750, 175, 1},
{1, 336, 7350, 19600, 7350, 336, 1},
{1, 588, 24696, 144060, 144060, 24696, 588, 1},
{1, 960, 70560, 790272, 1728720, 790272, 70560, 960, 1},
{1, 1485, 178200, 3492720, 14669424, 14669424, 3492720, 178200, 1485, 1},
{1, 2200, 408375, 13068000, 96049800, 184415616, 96049800, 13068000, 408375, 2200, 1}
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MATHEMATICA
| f[0, 0] = 1; f[n_, m_] := f[n, m] = Binomial[n, m]*Product[k!*(n + k)!/((m + k)!*(n - m + k)!), {k, 1, 2}]; t[n_, m_] = 2^(m - n)*f[n, m]*Sum[Binomial[n, k]*Binomial[k, m], {k, m, n}]; Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%]
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CROSSREFS
| Cf. A008459.
Sequence in context: A181543 A141696 A178122 * A168523 A144439 A157208
Adjacent sequences: A142467 A142468 A142469 * A142471 A142472 A142473
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KEYWORD
| nonn,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Sep 20 2008
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