A226804 Expansion of 1/((1-3x)(1-9x)(1-27x)(1-81x)).

1, 120, 10890, 914760, 74987451, 6098153040, 494603769780, 40080553611120, 3247001410058901, 263019982119962760, 21304965990387308670, 1725711626112542281080, 139782894999601166334351, 11322421333652608793333280, 917116312670388314093059560

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (120,-3510,29160,-59049).

Formula

G.f.: 1/((1-3*x)*(1-9*x)*(1-27*x)*(1-81*x)).

a(n) = 3^n*(3^(n+1)-1)*(3^(n+2)-1)*(3^(n+3)-1)/416.

a(0)=1, a(1)=120, a(2)=10890, a(3)=914760; for n>3, a(n) = 120*a(n-1) -3510*a(n-2) +29160*a(n-3) -59049*a(n-4).

a(n) -108*a(n-1) +2187*a(n-2) = A016142(n) with a(-1)=a(-2)=0. [Bruno Berselli, Jul 11 2013]

Mathematica

CoefficientList[Series[1 / ((1 - 3 x) (1 - 9 x) (1 - 27 x) (1 - 81 x)), {x, 0, 20}], x]
LinearRecurrence[{120, -3510, 29160, -59049}, {1, 120, 10890, 914760}, 20] (* Harvey P. Dale, Sep 21 2016 *)

Prog

(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-3*x)*(1-9*x)*(1-27*x)*(1-81*x)))); /* or */ I:=[1, 120, 10890, 914760]; [n le 4 select I[n] else 120*Self(n-1)-3510*Self(n-2)+29160*Self(n-3)-59049*Self(n-4): n in [1..25]];

Crossrefs

Cf. A000292, A016142, A028258.

Sequence in context: A218503 A221620 A299954 * A104592 A135379 A296913

Adjacent sequences: A226801 A226802 A226803 * A226805 A226806 A226807

Keyword

nonn,easy

Author

Vincenzo Librandi, Jul 11 2013

Status

approved