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%I #13 Apr 20 2024 13:44:53
%S 1,8,35,110,280,616,1218,2220,3795,6160,9581,14378,20930,29680,41140,
%T 55896,74613,98040,127015,162470,205436,257048,318550,391300,476775,
%U 576576,692433,826210,979910,1155680,1355816,1582768,1839145,2127720,2451435,2813406
%N Expansion of (1 + 2*x + 2*x^2) / (1 - x)^6.
%H Colin Barker, <a href="/A244882/b244882.txt">Table of n, a(n) for n = 0..1000</a>
%H R. P. Stanley, <a href="/A002721/a002721.pdf">Examples of Magic Labelings</a>, Unpublished Notes, 1973 [Cached copy, with permission]See page 33.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F G.f.: (1 + 2*x + 2*x^2) / (1 - x)^6.
%F From _Colin Barker_, Jan 12 2017: (Start)
%F a(n) = (24 + 62*n + 63*n^2 + 33*n^3 + 9*n^4 + n^5) / 24.
%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) for n>5.
%F (End)
%t CoefficientList[Series[(1+2x+2x^2)/(1-x)^6,{x,0,40}],x] (* or *) LinearRecurrence[{6,-15,20,-15,6,-1},{1,8,35,110,280,616},40] (* _Harvey P. Dale_, Dec 26 2016 *)
%o (PARI) Vec((1 + 2*x + 2*x^2) / (1 - x)^6 + O(x^40)) \\ _Colin Barker_, Jan 12 2017
%K nonn,easy,changed
%O 0,2
%A _N. J. A. Sloane_, Jul 08 2014
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