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%I #15 Sep 08 2022 08:45:49
%S 0,1,4352,807003,33685504,611328125,6535385856,48464682007,
%T 274945015808,1271126624409,5000500000000,17262535045811,
%U 53499182579712,151442855545813,396867717150464,973116755859375,2251834173423616,4952348310391217,10411581612480768
%N a(n) = n^9*(n^4 + 1)/2.
%H Vincenzo Librandi, <a href="/A170786/b170786.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (14, -91, 364, -1001, 2002, -3003, 3432, -3003, 2002, -1001, 364, -91,14, -1).
%F From _Colin Barker_, Dec 06 2017: (Start)
%F G.f.: x*(1 + 4338*x + 746166*x^2 + 22783130*x^3 + 211585215*x^4 + 752778228*x^5 + 1137716244*x^6 + 752778228*x^7 + 211585215*x^8 + 22783130*x^9 + 746166*x^10 + 4338*x^11 + x^12) / (1 - x)^14.
%F a(n) = 14*a(n-1) - 91*a(n-2) + 364*a(n-3) - 1001*a(n-4) + 2002*a(n-5) - 3003*a(n-6) + 3432*a(n-7) - 3003*a(n-8) + 2002*a(n-9) - 1001*a(n-10) + 364*a(n-11) - 91*a(n-12) - 14*a(n-13) + a(n-14) for n>13.
%F (End)
%t Table[n^9 (n^4+1)/2,{n,0,30}] (* or *) LinearRecurrence[{14, -91, 364, -1001, 2002, -3003, 3432, -3003,2002,-1001,364,-91,14,-1}, {0,1, 4352, 807003, 33685504,611328125 ,6535385856,48464682007, 274945015808, 1271126624409, 5000500000000, 17262535045811, 53499182579712, 151442855545813}, 30] (* _Harvey P. Dale_, Aug 22 2016 *)
%o (Magma) [n^9*(n^4+1)/2: n in [0..20]]; // _Vincenzo Librandi_, Aug 26 2011
%o (PARI) for(n=0, 30, print1(n^9*(n^4+1)/, ", ")) \\ _G. C. Greubel_, Dec 06 2017
%o (PARI) concat(0, Vec(x*(1 + 4338*x + 746166*x^2 + 22783130*x^3 + 211585215*x^4 + 752778228*x^5 + 1137716244*x^6 + 752778228*x^7 + 211585215*x^8 + 22783130*x^9 + 746166*x^10 + 4338*x^11 + x^12) / (1 - x)^14 + O(x^20))) \\ _Colin Barker_, Dec 06 2017
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_, Dec 11 2009
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