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%I #22 Oct 11 2024 17:17:28
%S 1,11,80,490,2751,14721,76630,392480,1990901,10041031,50466780,
%T 253122870,1267989451,6347088941,31756902530,158848951660,
%U 794438206401,3972771638451,19865600535880,99333230758850,496681840129751,2483456263849561,12417422517238830
%N Expansion of 1/((1-x)(1-2x)(1-3x)(1-5x)).
%H Vincenzo Librandi, <a href="/A021024/b021024.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (11,-41,61,-30).
%F a(n) = stirling2(n+4,4) + stirling2(n+4,5). - _Zerinvary Lajos_, Oct 04 2007
%F a(0)=1, a(1)=11, a(2)=80, a(3)=490; for n>3, a(n) = 11*a(n-1) -41*a(n-2) +61*a(n-3) -30*a(n-4). - _Vincenzo Librandi_, Jul 05 2013
%F a(n) = 8*a(n-1) -15*a(n-2) +2^n -1. - _Vincenzo Librandi_, Jul 05 2013
%F a(n) = (5^(n+3) - 6*3^(n+3) + 8*2^(n+3) - 3)/24. [_Yahia Kahloune_, Jul 07 2013]
%p with(combinat): seq(stirling2(n+4,4) +stirling2(n+4,5), n=0..23); # _Zerinvary Lajos_, Oct 04 2007
%t CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 3 x) (1 -5 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 05 2013 *)
%t LinearRecurrence[{11,-41,61,-30},{1,11,80,490},30] (* _Harvey P. Dale_, Oct 11 2024 *)
%o (Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-3*x)*(1-5*x)))); /* or */ I:=[1, 11, 80, 490]; [n le 4 select I[n] else 11*Self(n-1)-41*Self(n-2)+61*Self(n-3)-30*Self(n-4): n in [1..25]]; // _Vincenzo Librandi_, Jul 05 2013
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.