A021084 Expansion of 1/((1-x)(1-2x)(1-4x)(1-9x)).

1, 16, 179, 1766, 16545, 151572, 1374943, 12417922, 111935549, 1008117968, 9075855867, 81693883518, 735289682713, 6617786085004, 59560790560151, 536049978287354, 4824461257701237, 43420197132033480

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (16,-77,134,-72).

Formula

a(0)=1, a(1)=16; for n>1, a(n) = 13*a(n-1) -36*a(n-2)+ 2^n - 1. - Vincenzo Librandi, Jul 06 2013

a(0)=1, a(1)=16, a(2)=179, a(3)=1766; for n>3, a(n) = 16*a(n-1) -77*a(n-2) +134*a(n-3) -72*a(n-4). - Vincenzo Librandi, Jul 06 2013

a(n) = (3*9^(n+3) - 28*4^(n+3) + 60*2^(n+3) - 35)/840. [Yahia Kahloune, Jul 07 2013]

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 4 x) (1 - 9 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 06 2013 *)

Prog

(PARI) Vec(1/((1-x)*(1-2*x)*(1-4*x)*(1-9*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012
(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-4*x)*(1-9*x)))); /* or */ I:=[1, 16, 179, 1766]; [n le 4 select I[n] else 16*Self(n-1)-77*Self(n-2)+134*Self(n-3)-72*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 06 2013

Crossrefs

Cf. A016291.

Sequence in context: A002399 A255255 A181239 * A227557 A269202 A269103

Adjacent sequences: A021081 A021082 A021083 * A021085 A021086 A021087

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved