A021314 Expansion of 1/((1-x)*(1-2*x)*(1-10*x)*(1-11*x)).

1, 24, 401, 5796, 77637, 992880, 12310537, 149304732, 1781240813, 20982537576, 244696801713, 2830553706708, 32524979660629, 371663665151712, 4227189205549529, 47887970149917324, 540656560537946685, 6086111054806236888, 68336110491757363585, 765586104298219626180

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (24,-175,372,-220).

Formula

a(0)=1, a(1)=24, a(2)=401, a(3)=5796, a(n)=24*a(n-1)-175*a(n-2)+ 372*a(n-3)- 220*a(n-4). - Harvey P. Dale, May 21 2012

a(n) = (8*11^(n+3) - 10^(n+4) + 5*2^(n+4) - 8)/720. - Yahia Kahloune, Jul 07 2013

a(0)=1, a(1)=24; for n>1, a(n) = 21*a(n-1) -110*a(n-2) +2^n -1. - Vincenzo Librandi, Jul 09 2013

E.g.f.: exp(x)*(1331*exp(10*x) - 1250*exp(9*x) + 10*exp(x) - 1)/90. - Stefano Spezia, Dec 06 2024

Mathematica

CoefficientList[Series[1 / ((1 - x)(1 - 2 x) (1 - 10 x) (1 - 11 x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{24, -175, 372, -220}, {1, 24, 401, 5796}, 30] (* Harvey P. Dale, May 21 2012 *)

Prog

(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-10*x)*(1-11*x)))); // Vincenzo Librandi, Jul 09 2013
(Magma) I:=[1, 24, 401, 5796]; [n le 4 select I[n] else 24*Self(n-1)-175*Self(n-2)+372*Self(n-3)-220*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 09 2013

Crossrefs

Sequence in context: A020341 A021674 A019677 * A018206 A021304 A018092

Adjacent sequences: A021311 A021312 A021313 * A021315 A021316 A021317

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved