A023946 Expansion of 1/((1-x)(1-5x)(1-10x)(1-11x)).

1, 27, 488, 7434, 103215, 1353681, 17093182, 210149568, 2533379189, 30086951895, 353166486036, 4106992533462, 47398834914523, 543607880403069, 6201901277261450, 70443098125125516, 797096110863739617

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (27,-241,765,-550).

Formula

a(n) = (6*11^(n+3) - 8*10^(n+3) + 3*5^(n+3) -1)/360. [Yahia Kahloune, Jun 27 2013]

a(0)=1, a(1)=27, a(2)=488, a(3)=7434; for n>3, a(n) = 27*a(n-1) -241*a(n-2) +765*a(n-3) -550*a(n-4). - Vincenzo Librandi, Jul 12 2013

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 5 x) (1 - 10 x) (1 - 11 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 12 2013 *)
LinearRecurrence[{27, -241, 765, -550}, {1, 27, 488, 7434}, 20] (* Harvey P. Dale, Jan 14 2015 *)

Prog

(Magma) I:=[1, 27, 488, 7434]; [n le 4 select I[n] else 27*Self(n-1)-241*Self(n-2)+765*Self(n-3)-550*Self(n-4): n in [1..25]]; /* or */ m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-5*x)*(1-10*x)*(1-11*x)))); // Vincenzo Librandi, Jul 12 2013

Crossrefs

Sequence in context: A024114 A025982 A042408 * A020971 A023772 A020726

Adjacent sequences: A023943 A023944 A023945 * A023947 A023948 A023949

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved