A019483 Expansion of 1/((1-4x)(1-6x)(1-10x)).

1, 20, 276, 3280, 36176, 383040, 3962176, 40428800, 409195776, 4121666560, 41395966976, 415039672320, 4156893515776, 41607983022080, 416314385842176, 4164552265891840, 41653977398706176, 416590519605657600

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (20,-124,240).

Formula

a(n) = 4*4^n/3 -9*6^n/2 +25*10^n/6. - R. J. Mathar, Jun 29 2013

a(0)=1, a(1)=20, a(2)=276; for n>2, a(n) = 20*a(n-1) -124*a(n-2) +240*a(n-3). - Vincenzo Librandi, Jul 03 2013

a(n) = 16*a(n-1) -60*a(n-2) +4^n. - Vincenzo Librandi, Jul 03 2013

Mathematica

CoefficientList[Series[1 / ((1 - 4 x) (1 - 6 x) (1 - 10 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 03 2013 *)
LinearRecurrence[{20, -124, 240}, {1, 20, 276}, 20] (* Harvey P. Dale, Aug 15 2017 *)

Prog

(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-4*x)*(1-6*x)*(1-10*x)))); /* or */ I:=[1, 20, 276]; [n le 3 select I[n] else 20*Self(n-1)-124*Self(n-2)+240*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 03 2013

Crossrefs

Sequence in context: A021264 A025928 A004334 * A018056 A021234 A021474

Adjacent sequences: A019480 A019481 A019482 * A019484 A019485 A019486

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved