A022628 Expansion of 1/((1-x)*(1-5*x)*(1-8*x)*(1-11*x)).

1, 25, 418, 5898, 76059, 930003, 10996396, 127188916, 1449394837, 16348318701, 183083516694, 2039995806654, 22648876033135, 250810539522919, 2772306789414112, 30602539667823912, 337485446955075753, 3719200955052251457, 40966103582317693450, 451066307861295957490

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (25,-207,623,-440).

Formula

a(n) = (14*11^(n+3) - 40*8^(n+3) + 35*5^(n+3) - 9)/2520. - Yahia Kahloune, Jun 29 2013

a(0)=1, a(1)=25, a(2)=418, a(3)=5898; for n > 3, a(n) = 25*a(n-1) - 207*a(n-2) + 623*a(n-3) - 440*a(n-4). - Vincenzo Librandi, Jul 12 2013

Maple

[seq(coeftayl(1/((1-x)*(1-5*x)*(1-8*x)*(1-11*x)), x = 0, k), k=1..20)]; # Muniru A Asiru, Feb 17 2018

Mathematica

CoefficientList[Series[1/((1-x)*(1-5*x)*(1-8*x)*(1-11*x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 12 2013 *)
Table[(14*11^(n+3) -40*8^(n+3) +35*5^(n+3) -9)/2520, {n, 0, 30}] (* G. C. Greubel, feb 16 2018 *)
LinearRecurrence[{25, -207, 623, -440}, {1, 25, 418, 5898}, 20] (* Harvey P. Dale, May 23 2021 *)

Prog

(Magma) I:=[1, 25, 418, 5898]; [n le 4 select I[n] else 25*Self(n-1)-207*Self(n-2)+623*Self(n-3)-440*Self(n-4): n in [1..25]]; /* or */ m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-5*x)*(1-8*x)*(1-11*x)))); // Vincenzo Librandi, Jul 12 2013
(PARI) x='x+O('x^30); Vec(1/((1-x)*(1-5*x)*(1-8*x)*(1-11*x))) \\ G. C. Greubel, Feb 16 2018
(GAP) A022628:=List([0..20], n->(14*11^(n+3)-40*8^(n+3)+35*5^(n+3)-9)/2520); # Muniru A Asiru, Feb 17 2018

Crossrefs

Sequence in context: A022845 A023952 A025991 * A020838 A025975 A025953

Adjacent sequences: A022625 A022626 A022627 * A022629 A022630 A022631

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved