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Expansion of 1/((1-x)*(1-5*x)*(1-7*x)*(1-10*x)).
1

%I #22 Sep 08 2022 08:44:46

%S 1,23,352,4530,53151,590373,6335302,66471680,687035701,7029030723,

%T 71413230252,722053798830,7276293638251,73154751811073,

%U 734297855505202,7362269063785980,73757914933860801,738526673084931423

%N Expansion of 1/((1-x)*(1-5*x)*(1-7*x)*(1-10*x)).

%H Vincenzo Librandi, <a href="/A022454/b022454.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (23,-177,505,-350).

%F a(n) = (8*10^(n+3)-30*7^(n+3)+27*5^(n+3)-5)/1080. -_Yahia Kahloune_, May 22 2013

%F a(0)=1, a(1)=23, a(2)=352, a(3)=4530; for n>3, a(n) = 23*a(n-1) -177*a(n-2) +505*a(n-3) -350*a(n-4). - _Vincenzo Librandi_, Jul 12 2013

%t CoefficientList[Series[1 / ((1 - x) (1 - 5 x) (1 - 7 x) (1 - 10 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 12 2013 *)

%t LinearRecurrence[{23,-177,505,-350},{1,23,352,4530},20] (* _Harvey P. Dale_, Nov 07 2013 *)

%o (Magma) I:=[1, 23, 352, 4530]; [n le 4 select I[n] else 23*Self(n-1)-177*Self(n-2)+505*Self(n-3)-350*Self(n-4): n in [1..25]]; /* or */ m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-5*x)*(1-7*x)*(1-10*x)))); // _Vincenzo Librandi_, Jul 12 2013

%o (PARI) x='x+O('x^30); Vec(1/((1-x)*(1-5*x)*(1-7*x)*(1-10*x))) \\ _G. C. Greubel_, Feb 28 2018

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_