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A168308 The fifth left hand column of triangle A167591.

%I A168308 #11 Mar 03 2024 17:46:47
%S A168308 525,12396,162740,1537216,11589216,73898880,413745024,2087500800,
%T A168308 9672309504,41745859584,169680276480,655126331392,2419298385920,
%U A168308 8593269522432,29494166618112,98195558891520,318148898783232,1005877391523840,3110695891894272
%N A168308 The fifth left hand column of triangle A167591.
%H A168308 G. C. Greubel, <a href="/A168308/b168308.txt">Table of n, a(n) for n = 5..1000</a>
%H A168308 <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 A168308 a(n) = 2^n*(107*n^9 - 1824*n^8 + 14124*n^7 - 62538*n^6 + 165228*n^5 - 259476*n^4 + 241561*n^3 - 133542*n^2 + 36360*n)/241920.
%F A168308 G.f.: (1936*z^4 + 9696*z^3 + 9320*z^2 + 1896*z + 525)/(1-2*z)^10.
%F A168308 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 A168308 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-2).
%t A168308 LinearRecurrence[{20,-180,960,-3360,8064,-13440,15360,-11520,5120,-1024},{525, 12396, 162740, 1537216, 11589216, 73898880, 413745024, 2087500800, 9672309504, 41745859584}, 50] (* _G. C. Greubel_, Jul 17 2016 *)
%o A168308 (Magma) [2^n*(107*n^9-1824*n^8+14124*n^7-62538*n^6+ 165228*n^5-259476*n^4+241561*n^3-133542*n^2+ 36360*n)/241920: n in [5..30]]; // _Vincenzo Librandi_, Jul 18 2016
%Y A168308 Equals the fifth left hand column of triangle A167591.
%Y A168308 Other left hand columns are A001787, A167592, A167593 and A168307.
%K A168308 easy,nonn
%O A168308 5,1
%A A168308 _Johannes W. Meijer_, Nov 23 2009