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Search: id:A166344
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| A166344 |
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Coefficients of recursive differential polynomial:p(x,3)=x*(x^2 + 6*x + 1)/(1 - x)^4;p(x, n) = x*D[p[x, n - 1], x] |
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+0
1
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| 1, 1, 1, 1, 6, 1, 1, 15, 15, 1, 1, 34, 90, 34, 1, 1, 73, 406, 406, 73, 1, 1, 152, 1583, 3248, 1583, 152, 1, 1, 311, 5661, 20907, 20907, 5661, 311, 1, 1, 630, 19160, 117594, 209070, 117594, 19160, 630, 1, 1, 1269, 62520, 604496, 1750914, 1750914, 604496, 62520
(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, 8, 32, 160, 960, 6720, 53760, 483840, 4838400, 53222400,...}
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REFERENCES
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Douglas C. Montgomery and Lynwood A. Johnson, Forecasting and Time Series Analysis, MaGraw-Hill, New York, 1976, page 91
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FORMULA
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p(x,0)= 1/(1 - x);
p(x,1)= x/(1 - x)^2;
p(x,2)= x*(1 + x)/(1 - x)^3;
p(x,3)= x*(x^2 + 6*x + 1)/(1 - x)^4;
p(x,n)= x*D[p[x, n - 1], x]
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EXAMPLE
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{1},
{1, 1},
{1, 6, 1},
{1, 15, 15, 1},
{1, 34, 90, 34, 1},
{1, 73, 406, 406, 73, 1},
{1, 152, 1583, 3248, 1583, 152, 1},
{1, 311, 5661, 20907, 20907, 5661, 311, 1},
{1, 630, 19160, 117594, 209070, 117594, 19160, 630, 1},
{1, 1269, 62520, 604496, 1750914, 1750914, 604496, 62520, 1269, 1},
{1, 2548, 198981, 2918144, 12986042, 21010968, 12986042, 2918144, 198981, 2548, 1}
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MATHEMATICA
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p[x_, 0] := 1/(1 - x);
p[x_, 1] := x/(1 - x)^2;
p[x_, 2] := x*(1 + x)/(1 - x)^3;
p[x_, 3] := x*(x^2 + 6*x + 1)/(1 - x)^4;
p[x_, n_] := p[x, n] = x*D[p[x, n - 1], x]
a = Table[CoefficientList[FullSimplify[ExpandAll[(1 - x)^(n + 1)*p[x, n]/x]], x], {n, 1, 11}];
Flatten[a]
Table[Apply[Plus, CoefficientList[FullSimplify[ExpandAll[(1 - x)^(n + 1)*p[x, n]/x]], x]], {n, 1, 11}];
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CROSSREFS
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A123125
Sequence in context: A152238 A086645 A154980 this_sequence A146766 A146958 A154653
Adjacent sequences: A166341 A166342 A166343 this_sequence A166345 A166346 A166347
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KEYWORD
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nonn,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Oct 12 2009
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