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A166343 Coefficients of recursive differential polynomial:p(x,3)=x*(x^2 + 12*x + 1)/(1 - x)^4;p(x, n) = x*D[p[x, n - 1], x] 1
1, 1, 1, 1, 12, 1, 1, 27, 27, 1, 1, 58, 162, 58, 1, 1, 121, 718, 718, 121, 1, 1, 248, 2759, 5744, 2759, 248, 1, 1, 503, 9765, 36771, 36771, 9765, 503, 1, 1, 1014, 32816, 205674, 367710, 205674, 32816, 1014, 1, 1, 2037, 106560, 1052408, 3072594, 3072594 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Row sums are:{1, 2, 14, 56, 280, 1680, 11760, 94080, 846720, 8467200, 93139200,...}

REFERENCES

Douglas C. Montgomery and Lynwood A. Johnson, Forecasting and Time Series Analysis, MaGraw-Hill, New York, 1976, page 91

LINKS

Table of n, a(n) for n=1..51.

FORMULA

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 + 12*x + 1)/(1 - x)^4;

p(x,n)= x*D[p[x, n - 1], x]

EXAMPLE

{1},

{1, 1},

{1, 12, 1},

{1, 27, 27, 1},

{1, 58, 162, 58, 1},

{1, 121, 718, 718, 121, 1},

{1, 248, 2759, 5744, 2759, 248, 1},

{1, 503, 9765, 36771, 36771, 9765, 503, 1},

{1, 1014, 32816, 205674, 367710, 205674, 32816, 1014, 1},

{1, 2037, 106560, 1052408, 3072594, 3072594, 1052408, 106560, 2037, 1},

{1, 4084, 338013, 5062112, 22729826, 36871128, 22729826, 5062112, 338013, 4084, 1}

MATHEMATICA

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 + 12*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}];

CROSSREFS

A123125

Sequence in context: A168646 A051457 A174450 * A186432 A176489 A174039

Adjacent sequences:  A166340 A166341 A166342 * A166344 A166345 A166346

KEYWORD

nonn,uned

AUTHOR

Roger L. Bagula, Oct 12 2009

STATUS

approved

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Last modified September 20 01:32 EDT 2020. Contains 337244 sequences. (Running on oeis4.)