%I #17 Jul 30 2022 19:15:00
%S -2,-7,-15,-25,-35,-42,-42,-30,0,55,143,273,455,700,1020,1428,1938,
%T 2565,3325,4235,5313,6578,8050,9750,11700,13923,16443,19285,22475,
%U 26040,30008,34408,39270,44625,50505,56943,63973,71630,79950,88970,98728,109263,120615
%N a(n) = (n-5)*(n-6)*(n-7)*(n-16)/24.
%H G. C. Greubel, <a href="/A167543/b167543.txt">Table of n, a(n) for n = 8..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
%F G.f.: x^8*(-2+3*x)/(1-x)^5.
%F E.g.f.: (1/24)*( -3360 - 1800*x - 420*x^2 - 52*x^3 - 3*x^4 + (3360 - 1560*x + 300*x^2 - 28*x^3 + x^4)*exp(x) ). - _G. C. Greubel_, Jul 30 2022
%t Table[(n-5)*(n-6)*(n-7)*(n-16)/24, {n,8,60}] (* _G. C. Greubel_, Jun 15 2016 *)
%o (Magma) [Binomial(n-5,3)*(n-16)/4: n in [8..60]]; // _G. C. Greubel_, Jul 30 2022
%o (SageMath) [binomial(n-5,3)*(n-16)/4 for n in (8..60)] # _G. C. Greubel_, Jul 30 2022
%Y Cf. A111373, A135929, A137276.
%K sign,easy
%O 8,1
%A _Jamel Ghanouchi_, Nov 06 2009
%E Definition simplified, sequence extended by _R. J. Mathar_, Nov 12 2009
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