A021074 Expansion of 1/((1-x)(1-2x)(1-4x)(1-5x)).

1, 12, 95, 630, 3801, 21672, 119155, 639210, 3370301, 17549532, 90541815, 463889790, 2364180001, 11999840592, 60714998075, 306438236370, 1543644296901, 7764034206852, 39003422447935

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (12,-49,78,-40).

Formula

a(0)=1, a(1)=12, a(2)=95, a(3)=630, a(n)=12*a(n-1)-49*a(n-2)+78*a(n-3)-40*a(n-4). [Harvey P. Dale, Oct 01 2011]

a(n) = (5^(n+3) - 2*4^(n+3) + 2*2^(n+3) - 1)/12. [Yahia Kahloune, Apr 29 2013]

a(0)=1, a(1)=12; for n>1, a(n) = 9*a(n-1) -20*a(n-2) + 2^n - 1. - Vincenzo Librandi, Jul 05 2013

Mathematica

CoefficientList[Series[1/((1-x)(1-2x)(1-4x)(1-5x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{12, -49, 78, -40}, {1, 12, 95, 630}, 30] (* Harvey P. Dale, Oct 01 2011 *)

Prog

(Magma) I:=[1, 12]; [n le 2 select I[n] else 9*Self(n-1)-20*Self(n-2)+2^n-1: n in [1..25]]; /* or */ m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-4*x)*(1-5*x)))); // Vincenzo Librandi, Jul 05 2013

Crossrefs

Sequence in context: A009647 A038836 A026860 * A027250 A194782 A059154

Adjacent sequences: A021071 A021072 A021073 * A021075 A021076 A021077

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved