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A028219

Expansion of 1/((1 - 6*x)*(1 - 10*x)*(1 - 11*x)*(1 - 12*x)).

1, 39, 961, 19131, 336217, 5446035, 83308177, 1221791547, 17352006793, 240304555491, 3261449180353, 43542585627723, 573464912457529, 7467052092622707, 96294712139682289, 1231626797709018459

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OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..900

Index entries for linear recurrences with constant coefficients, signature (39,-560,3492,-7920).

FORMULA

a(n) = 23*a(n-1) - 132*a(n-2) + 2^(n-1)*(5^(n+1) - 3^(n+1)), n >= 2. - Vincenzo Librandi, Mar 13 2011

a(n) = (5*12^(n+2) - 11^(n+3) + 5^4*10^n - 9*6^n)/5. - R. J. Mathar, Mar 15 2011

E.g.f.: (720*exp(12*x) -1331*exp(11*x) + 625*exp(10*x) -9*exp(6*x))/5. - G. C. Greubel, Oct 28 2019

MAPLE

seq((5*12^(n+2) + 5^4*10^n - 9*6^n - 11^(n+3))/5, n=0..30); # G. C. Greubel, Oct 28 2019

MATHEMATICA

CoefficientList[Series[1/((1 - 6x)(1 - 10x)(1 - 11x)(1 - 12x)) , {x, 0, 29}], x] (* Alonso del Arte, Oct 25 2019 *)

LinearRecurrence[{39, -560, 3492, -7920}, {1, 39, 961, 19131}, 20] (* Harvey P. Dale, Jan 26 2026 *)

PROG

(PARI) vector(31, n, (5*12^(n+1) +5^4*10^(n-1) -9*6^(n-1) -11^(n+2))/5) \\ G. C. Greubel, Oct 28 2019

(Magma) [(5*12^(n+2) + 5^4*10^n - 9*6^n - 11^(n+3))/5: n in [0..30]]; // G. C. Greubel, Oct 28 2019

(SageMath) [(5*12^(n+2) + 5^4*10^n - 9*6^n - 11^(n+3))/5 for n in (0..30)] # G. C. Greubel, Oct 28 2019

(GAP) List([0..30], n-> (5*12^(n+2) + 5^4*10^n - 9*6^n - 11^(n+3))/5); # G. C. Greubel, Oct 28 2019

CROSSREFS

Sequence in context: A194477 A016091 A028227 * A209076 A251327 A014936

Adjacent sequences: A028216 A028217 A028218 * A028220 A028221 A028222

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

URL: https://oeis.org/A028219

⇱ A028219 - OEIS