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Expansion of 1/((1-7*x)*(1-10*x)*(1-12*x)).
1

%I #27 Dec 31 2024 06:36:15

%S 1,29,567,9337,139775,1971417,26715823,352001609,4543901439,

%T 57765992185,725866130639,9039113138601,111770394659743,

%U 1374351994892633,16823974751541615,205209952708309513,2495775222328385087,30282093196741317561,366714652062500686351

%N Expansion of 1/((1-7*x)*(1-10*x)*(1-12*x)).

%H G. C. Greubel, <a href="/A020974/b020974.txt">Table of n, a(n) for n = 0..922</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (29,-274,840).

%F a(n) = 29*a(n-1) - 274*a(n-2) + 840*a(n-3) for n>=3. - _Vincenzo Librandi_, Mar 15 2011

%F a(n) = 22*a(n-1) - 120*a(n-2) + 7^n for n>1 a(0)=1, a(1)=29. - _Vincenzo Librandi_, Mar 15 2011

%F a(n) = (3*12^(n+2) - 5*10^(n+2) + 2*7^(n+2))/30. - _Yahia Kahloune_, Jun 30 2013

%t CoefficientList[Series[1/((1-7x)(1-10x)(1-12 x)), {x,0,50}], x] (* _G. C. Greubel_, May 31 2018 *)

%t LinearRecurrence[{29,-274,840},{1,29,567},30] (* _Harvey P. Dale_, Apr 25 2020 *)

%o (PARI) my(x='x+O('x^30)); Vec(1/((1-7*x)*(1-10*x)*(1-12*x))) \\ _G. C. Greubel_, May 31 2018

%o (Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-7*x)*(1-10*x)*(1-12*x)))); // _G. C. Greubel_, May 31 2018

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_

%E Terms a(16) onward added by _G. C. Greubel_, May 31 2018