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Search: id:A141686
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| A141686 |
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Symmetrical triangular sequence of coefficients: Eulerian numbers times Pascal's triangle: t(n,m)=A008292(n,m)*Binomial(n,m). |
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+0
1
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| 1, 1, 1, 1, 8, 1, 1, 33, 33, 1, 1, 104, 396, 104, 1, 1, 285, 3020, 3020, 285, 1, 1, 720, 17865, 48320, 17865, 720, 1, 1, 1729, 90153, 546665, 546665, 90153, 1729, 1, 1, 4016, 409024, 4941104, 10933300, 4941104, 409024, 4016, 1, 1, 9117, 1722240, 38236128
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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Row sums are:
{1, 2, 10, 68, 606, 6612, 85492, 1277096, 21641590, 410144180}.
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REFERENCES
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Weisstein, Eric W."Eulerian Number."http : // mathworld.wolfram.com/EulerianNumber.html
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FORMULA
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t(n,m)=A008292(n,m)*Binomial(n,m).
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EXAMPLE
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{1},
{1, 1},
{1, 8, 1},
{1, 33, 33, 1},
{1, 104, 396, 104, 1},
{1, 285, 3020, 3020, 285, 1},
{1, 720, 17865, 48320, 17865, 720, 1},
{1, 1729, 90153, 546665, 546665, 90153, 1729, 1},
{1, 4016, 409024, 4941104, 10933300, 4941104, 409024, 4016, 1},
{1, 9117, 1722240, 38236128, 165104604, 165104604, 38236128, 1722240, 9117, 1}
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MATHEMATICA
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(*Recurrence*) A[n_, 1] := 1; A[n_, n_] := 1; A[n_, k_] := (n - k + 1)A[n - 1, k - 1] + k A[n - 1, k]; Table[Table[A[n, k]*Binomial[n - 1, k - 1], {k, 1, n}], {n, 1, 10}]; Flatten[%]
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CROSSREFS
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Cf. A008292.
Sequence in context: A142470 A144439 A157208 this_sequence A157148 A154335 A142467
Adjacent sequences: A141683 A141684 A141685 this_sequence A141687 A141688 A141689
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KEYWORD
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nonn,uned
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AUTHOR
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Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Sep 08 2008
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