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%I #29 Sep 08 2022 08:44:49
%S 1,2,5,13,33,79,176,365,709,1300,2267,3785,6085,9465,14302,21065,
%T 30329,42790,59281,80789,108473,143683,187980,243157,311261,394616,
%U 495847,617905,764093,938093,1143994,1386321,1670065,2000714
%N a(n) = T(n, 2*n-6), T given by A027926.
%H Vincenzo Librandi, <a href="/A027929/b027929.txt">Table of n, a(n) for n = 3..1000</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F a(n) = Sum_{k=0..3} binomial(n-k, 6-2*k). - _Len Smiley_, Oct 20 2001
%F From _Colin Barker_, May 01 2012: (Start)
%F a(n) = (3600 -3420*n +1684*n^2 -525*n^3 +115*n^4 -15*n^5 +n^6)/720.
%F G.f.: x^3*(1-x+x^2)*(1-4*x+7*x^2-4*x^3+x^4)/(1-x)^7. (End)
%F E.g.f.: (3600 - 2160*x + 720*x^2 - 120*x^3 + 30*x^4 + x^6)*exp(x)/720 - 5 + 2*x - x^2/2. - _G. C. Greubel_, Sep 06 2019
%p seq((3600 -3420*n +1684*n^2 -525*n^3 +115*n^4 -15*n^5 +n^6)/720, n=3..40); # _G. C. Greubel_, Sep 06 2019
%t CoefficientList[Series[(1-x+x^2)(1-4x+7x^2-4x^3+x^4)/(1-x)^7, {x, 0, 40}], x] (* _Vincenzo Librandi_, Oct 18 2013 *)
%o (PARI) vector(40, n, m=n+2; (3600 -3420*m +1684*m^2 -525*m^3 +115*m^4 -15*m^5 +m^6)/720) \\ _G. C. Greubel_, Sep 06 2019
%o (Magma) [(3600 -3420*n +1684*n^2 -525*n^3 +115*n^4 -15*n^5 +n^6)/720: n in [3..40]]; // _G. C. Greubel_, Sep 06 2019
%o (Sage) [(3600 -3420*n +1684*n^2 -525*n^3 +115*n^4 -15*n^5 +n^6)/720 for n in (3..40)] # _G. C. Greubel_, Sep 06 2019
%o (GAP) List([3..40], n-> (3600 -3420*n +1684*n^2 -525*n^3 +115*n^4 -15*n^5 +n^6)/720); _G. C. Greubel_, Sep 06 2019
%Y Cf. A228074.
%K nonn,easy
%O 3,2
%A _Clark Kimberling_
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