login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A166346 Coefficients of recursive differential polynomial:p(x,3)=x*(x^2 + 8*x + 1)/(1 - x)^4;p(x, n) = 2*x*D[p(x, n - 1), x]-p(x,n-2) 5
1, 1, 1, 1, 8, 1, 1, 39, 39, 1, 1, 158, 482, 158, 1, 1, 605, 4194, 4194, 605, 1, 1, 2276, 31047, 67752, 31047, 2276, 1, 1, 8515, 210609, 856075, 856075, 210609, 8515, 1, 1, 31802, 1356368, 9367974, 17194910, 9367974, 1356368, 31802, 1, 1, 118713 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Row sums are:{1, 2, 10, 80, 800, 9600, 134400, 2150400, 38707200, 774144000, 17031168000,...}

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..47.

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 +8*x + 1)/(1 - x)^4;

p(x,n)= 2*x*D[p[x, n - 1], x] - p[x, n - 2]

EXAMPLE

{1},

{1, 1},

{1, 8, 1},

{1, 39, 39, 1},

{1, 158, 482, 158, 1},

{1, 605, 4194, 4194, 605, 1},

{1, 2276, 31047, 67752, 31047, 2276, 1},

{1, 8515, 210609, 856075, 856075, 210609, 8515, 1},

{1, 31802, 1356368, 9367974, 17194910, 9367974, 1356368, 31802, 1},

{1, 118713, 8453460, 93489572, 285010254, 285010254, 93489572, 8453460, 118713, 1},

{1, 443072, 51564829, 876484896, 4159141218, 6855899968, 4159141218, 876484896, 51564829, 443072, 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 + 8*x + 1)/(1 - x)^4;

p[x_, n_] := p[x, n] = 2*x*D[p[x, n - 1], x] - p[x, n - 2]

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, A142458

Sequence in context: A142597 A156137 A152972 * A157640 A142458 A174528

Adjacent sequences:  A166343 A166344 A166345 * A166347 A166348 A166349

KEYWORD

nonn,uned

AUTHOR

Roger L. Bagula, Oct 12 2009

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 7 12:47 EDT 2022. Contains 355148 sequences. (Running on oeis4.)