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

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 *)

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
(Sage) [(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