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%I #28 Jun 13 2023 09:04:50
%S 0,0,0,0,1,6,18,42,84,151,252,396,594,858,1201,1638,2184,2856,3672,
%T 4651,5814,7182,8778,10626,12751,15180,17940,21060,24570,28501,32886,
%U 37758,43152,49104,55651,62832,70686,79254,88578,98701
%N a(n) = floor(n(n-1)(n-2)(n-3)/20).
%H Vincenzo Librandi, <a href="/A011930/b011930.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (4, -6, 4, -1, 1, -4, 6, -4, 1).
%F From _R. J. Mathar_, Apr 15 2010: (Start)
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) + a(n-5) - 4*a(n-6) + 6*a(n-7) - 4*a(n-8) + a(n-9).
%F G.f.: x^4*(x^4+2*x^3+2*x+1) / ((1-x)^5*(x^4+x^3+x^2+x+1)). (End)
%t CoefficientList[Series[x^4*(x^4+2*x^3+2*x+1)/((1-x)^5*(x^4+x^3+x^2+x+1)),{x,0,50}],x] (* _Vincenzo Librandi_, Jun 19 2012 *)
%t Table[Floor[n(n-1)(n-2)(n-3)/20],{n,0,40}] (* or *) LinearRecurrence[ {4,-6,4,-1,1,-4,6,-4,1},{0,0,0,0,1,6,18,42,84},40] (* _Harvey P. Dale_, Apr 08 2013 *)
%o (Magma) [Floor(n*(n-1)*(n-2)*(n-3)/20 ): n in [0..40]]; // _Vincenzo Librandi_, Jun 19 2012
%K nonn,easy
%O 0,6
%A _N. J. A. Sloane_