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a(n) = n^4*(n^9 + 1)/2.
1

%I #17 Sep 08 2022 08:45:49

%S 0,1,4104,797202,33554560,610351875,6530347656,48444506404,

%T 274877908992,1270932917445,5000000005000,17261356079286,

%U 53496602699904,151437553310407,396857386646280,973097534205000,2251799813718016

%N a(n) = n^4*(n^9 + 1)/2.

%H Vincenzo Librandi, <a href="/A168345/b168345.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 G.f.: x*(1 + 4090*x + 739837*x^2 + 22766832*x^3 + 211640562*x4 + 752810940*x^5 + 1137586002*x^6 + 752810568*x^7 + 211640973*x^8 + 22766618*x^9 + 739889*x^10 + 4088*x^11)/(1 - x)^14. - _Ilya Gutkovskiy_, Jul 19 2016

%t Table[ n^4*(n^9 + 1)/2 , {n,0,50}] (* _G. C. Greubel_, Jul 18 2016 *)

%t LinearRecurrence[{14,-91,364,-1001,2002,-3003,3432,-3003,2002,-1001,364,-91,14,-1},{0,1,4104,797202,33554560,610351875,6530347656,48444506404,274877908992,1270932917445,5000000005000,17261356079286,53496602699904,151437553310407},50] (* _Harvey P. Dale_, May 12 2018 *)

%o (Magma) [n^4*(n^9+1)/2: n in [0..20]]; // _Vincenzo Librandi_, Aug 28 2011

%o (PARI) a(n)=n^4*(n^9+1)/2 \\ _Charles R Greathouse IV_, Jul 19 2016

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_, Dec 11 2009