%I #11 Mar 03 2024 17:44:15
%S 105,6534,132444,1593960,13962848,98382912,590814336,3137815296,
%T 15114950400,67240622592,279977837568,1102376491008,4137416245248,
%U 14896905748480,51722619518976,173913487048704,568323403481088,1810359422681088,5635647921192960
%N The fifth left hand column of triangle A167580.
%H G. C. Greubel, <a href="/A168306/b168306.txt">Table of n, a(n) for n = 5..1000</a>
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (20, -180, 960, -3360, 8064, -13440, 15360, -11520, 5120, -1024).
%F a(n) = 2^n*(214*n^9 - 3963*n^8 + 30768*n^7 - 130536*n^6 + 330834*n^5 - 514332*n^4 + 484382*n^3 - 262149*n^2 + 72342*n - 7560)/241920.
%F G.f.: (32*z^5 + 3728*z^4 + 20400*z^3 + 20664*z^2 + 4434*z + 105)/(2*z-1)^10.
%F a(n) = 20*a(n-1) - 180*a(n-2) + 960*a(n-3) - 3360*a(n-4) + 8064*a(n-5) - 13440*a(n-6) + 15360*a(n-7) - 11520*a(n-8) + 5120*a(n-9) - 1024*a(n-10).
%F a(n) - 19*a(n-1) + 162*a(n-2) - 816*a(n-3) + 2688*a(n-4) - 6048*a(n-5) + 9408*a(n-6) - 9984*a(n-7) + 6912*a(n-8) - 2816*a(n-9) + 512*a(n-10) = 321*2^(n-1).
%t LinearRecurrence[{20,-180,960,-3360,8064,-13440,15360,-11520,5120,-1024},{105, 6534, 132444, 1593960, 13962848, 98382912, 590814336, 3137815296, 15114950400, 67240622592},50] (* _G. C. Greubel_, Jul 17 2016 *)
%o (Magma) [2^n*(214*n^9-3963*n^8+30768*n^7-130536*n^6+ 330834*n^5-514332*n^4+484382*n^3-262149*n^2+72342*n- 7560)/241920: n in [5..40]]; // _Vincenzo Librandi_, Jul 18 2016
%Y Equals the fifth left hand column of triangle A167580.
%Y Other left hand columns are A014480, A167581, A167582 and A168305.
%K easy,nonn
%O 5,1
%A _Johannes W. Meijer_, Nov 23 2009