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A026738 Expansion of 1/((1-2*x)*(1-6*x)*(1-8*x)*(1-12*x)). 1
1, 28, 516, 7952, 111440, 1477056, 18912832, 236879104, 2924469504, 35764112384, 434623874048, 5259666886656, 63472710995968, 764545789837312, 9197653087371264, 110557371200503808, 1328176959287263232, 15950056940486000640, 191496303058077614080 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..915

Index entries for linear recurrences with constant coefficients, signature (28,-268,1008,-1152).

FORMULA

a(n) = (18*12^(n + 1) - 5*8^(n + 2) + 135*6^n - 2^n)/30. - R. J. Mathar, Jun 23 2013

a(0) = 1, a(1)=28, a(2)=516, a(3)=7952, a(n) = 28*a(n-1) - 268*a(n-2) + 1008*a(n-3) - 1152*a(n-4). - Harvey P. Dale, Jul 25 2013

E.g.f.: (-exp(2*x) + 135*exp(6*x) - 320*exp(8*x) + 216*exp(12*x))/30. - G. C. Greubel, Oct 26 2019

MAPLE

A026738:= n-> (18*12^(n+1) -5*8^(n+2) +135*6^n -2^n)/30: seq(A026738(n), n=0..30); # Wesley Ivan Hurt, Feb 15 2014

MATHEMATICA

CoefficientList[Series[1/((1-2x)(1-6x)(1-8x)(1-12x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{28, -268, 1008, -1152}, {1, 28, 516, 7952}, 30] (* Harvey P. Dale, Jul 25 2013 *)

PROG

(PARI) vector(31, n, (18*12^n -5*8^(n+1) +135*6^(n-1) -2^(n-1))/30) \\ G. C. Greubel, Oct 26 2019

(MAGMA) [(18*12^(n+1) -5*8^(n+2) +135*6^n -2^n)/30: n in [0..30]]; // G. C. Greubel, Oct 26 2019

(Sage) [(18*12^(n+1) -5*8^(n+2) +135*6^n -2^n)/30 for n in (0..30)] # G. C. Greubel, Oct 26 2019

(GAP) List([0..30], n-> (18*12^(n+1) -5*8^(n+2) +135*6^n -2^n)/30); # G. C. Greubel, Oct 26 2019

CROSSREFS

Sequence in context: A028067 A024771 A028050 * A026149 A028049 A283244

Adjacent sequences:  A026735 A026736 A026737 * A026739 A026740 A026741

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified July 2 10:39 EDT 2022. Contains 355004 sequences. (Running on oeis4.)