A021268 Expansion of 1/((1-x)(1-2x)(1-8x)(1-10x)).

1, 21, 305, 3825, 44481, 494721, 5346625, 56661825, 592183361, 6126355521, 62899732545, 642086748225, 6525582872641, 66093551865921, 667637303808065, 6729987319337025, 67728787443552321, 680719188437241921

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (21,-136,276,-160).

Formula

a(n) = (7*10^(n+3) - 12*8^(n+3) + 21*2^(n+3) - 16)/1008. [Yahia Kahloune, Jun 30 2013]

a(0)=1, a(1)=21, a(2)=305, a(3)=3825; for n>3, a(n) = 21*a(n-1) -136*a(n-2) +276*a(n-3) -160*a(n-4). - Vincenzo Librandi, Jul 08 2013

a(0)=1, a(1)=21; for n>1, a(n) = 18*a(n-1) -80*a(n-2) +2^n -1. - Vincenzo Librandi, Jul 08 2013

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 8 x) (1 - 10 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 08 2013 *)

Prog

(Magma) I:=[1, 21, 305, 3825]; [n le 4 select I[n] else 21*Self(n-1)-136*Self(n-2)+276*Self(n-3)-160*Self(n-4): n in [1..25]]; /* or */ m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-8*x)*(1-10*x)))); // Vincenzo Librandi, Jul 08 2013

Crossrefs

Sequence in context: A019618 A081553 A021524 * A018069 A019488 A025929

Adjacent sequences: A021265 A021266 A021267 * A021269 A021270 A021271

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved