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%I #14 Sep 08 2022 08:46:01
%S 1,-4,37,-232,1705,-11692,82573,-575824,4037329,-28241620,197750389,
%T -1384075576,9689060473,-67821828988,474757585885,-3323288752288,
%U 23263064312737,-162841321048996,1139889634763461,-7979226281082760,55854587454363721,-390982101720192844
%N Expansion of 1/((1-3*x)*(1+7*x)).
%H Bruno Berselli, <a href="/A201865/b201865.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (-4,21).
%F G.f.: 1/((1-3*x)*(1+7*x)).
%F a(n) = (3^(n+1)+7*(-7)^n)/10.
%F a(n) = -4*a(n-1)+21*a(n-2) with n>0, a(-1)=0, a(0)=1.
%F a(n)-a(n-1) = A083300(n)*(-1)^n.
%F a(n)+5*a(n-1) = A083296(n) with a(-1)=0.
%t CoefficientList[Series[1/((1-3*x)*(1+7*x)), {x, 0, 22}], x]
%o (PARI) Vec(1/((1-3*x)*(1+7*x))+O(x^22))
%o (Magma) m:=22; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-3*x)*(1+7*x))));
%o (Maxima) makelist(coeff(taylor(1/((1-3*x)*(1+7*x)), x, 0, n), x, n), n, 0, 21);
%Y Cf. A014986, A083296, A083300.
%K sign,easy
%O 0,2
%A _Bruno Berselli_, Dec 07 2011
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