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Expansion of (1-x)/( (1+x)*(1-2*x)*(1-3*x)*(1-4*x)).
2

%I #17 Sep 08 2022 08:44:32

%S 1,7,39,191,875,3843,16423,68887,285219,1170059,4768127,19336863,

%T 78141883,314953555,1266977751,5089412519,20422176467,81882328731,

%U 328110270895,1314184126255,5261965982571,21063553061987

%N Expansion of (1-x)/( (1+x)*(1-2*x)*(1-3*x)*(1-4*x)).

%H Vincenzo Librandi, <a href="/A004057/b004057.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (8,-17,-2,24).

%F a(n) = (1/30)*(20*2^n - 135*3^n + 144*4^n + (-1)^n).

%t CoefficientList[Series[(1-x)/((1+x)(1-2x)(1-3x)(1-4x)),{x,0,30}],x] (* or *) LinearRecurrence[{8,-17,-2,24},{1,7,39,191},30] (* _Harvey P. Dale_, Oct 22 2019 *)

%o (Magma) [(1/30)* (20*2^n - 135*3^n + 144*4^n + (-1)^n): n in [0..30]]; // _Vincenzo Librandi_, Oct 08 2011

%Y First differences of A099110.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_