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%I #20 Sep 08 2022 08:44:59
%S 2,8,24,60,131,258,469,800,1296,2012,3014,4380,6201,8582,11643,15520,
%T 20366,26352,33668,42524,53151,65802,80753,98304,118780,142532,169938,
%U 201404,237365,278286,324663,377024,435930,501976,575792,658044,749435,850706,962637
%N a(n) = n*(n^4 + 10*n^3 + 35*n^2 + 50*n + 144)/120.
%H Colin Barker, <a href="/A051745/b051745.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F a(n) = binomial(n+4, n-1) + binomial(n, n-1).
%F a(n) = C(n+4, 5) + n = A000389(n+4) + n.
%F a(n) = 6*a(n-1)-15*a(n-2)+20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6), with a(1)=2, a(2)=8, a(3)=24, a(4)=60, a(5)=131, a(6)=258. - _Harvey P. Dale_, Apr 07 2013
%F G.f.: x*(x^4-4*x^3+6*x^2-4*x+2) / (x-1)^6. - _Colin Barker_, Mar 19 2015
%F E.g.f.: x*(240 + 240*x + 120*x^2 + 20*x^3 + x^4)*exp(x)/120. - _G. C. Greubel_, Nov 25 2017
%t Table[Binomial[n+4,n-1]+Binomial[n,n-1],{n,40}] (* or *) LinearRecurrence[ {6,-15,20,-15,6,-1},{2,8,24,60,131,258},40] (* _Harvey P. Dale_, Apr 07 2013 *)
%o (PARI) Vec(x*(x^4-4*x^3+6*x^2-4*x+2)/(x-1)^6 + O(x^100)) \\ _Colin Barker_, Mar 19 2015
%o (Magma) [n*(n^4 + 10*n^3 + 35*n^2 + 50*n + 144)/120: n in [1..30]]; // _G. C. Greubel_, Nov 25 2017
%K easy,nonn
%O 1,1
%A Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 07 1999
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