Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #15 Sep 08 2022 08:45:49
%S 0,1,544,29889,526336,4890625,30256416,141296449,537001984,1743657921,
%T 5000500000,12969598081,30960175104,68931659329,144631092256,
%U 288330890625,549764202496,1008009019009,1785250619424,3065556651841
%N a(n) = n^6*(n^4 + 1)/2.
%H Vincenzo Librandi, <a href="/A168564/b168564.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
%F G.f.: (x + 533*x^2 + 23960*x^3 + 227312*x^4 + 655394*x^5 + 655394*x^6 + 227312*x^7 + 23960*x^8 + 533*x^9 + x^10)/(1 - x)^11. - _G. C. Greubel_, Jul 26 2016
%t Table[n^6*( n^4 + 1)/2, {n,0,25}] (* _G. C. Greubel_, Jul 26 2016 *)
%t CoefficientList[Series[(x+533x^2+23960x^3+227312x^4+655394x^5+655394x^6+227312x^7+23960x^8+533x^9+x^10)/(1-x)^11,{x,0,30}],x] (* or *) LinearRecurrence[ {11,-55,165,-330,462,-462,330,-165,55,-11,1},{0,1,544,29889,526336,4890625,30256416,141296449,537001984,1743657921,5000500000},40] (* _Harvey P. Dale_, Aug 06 2021 *)
%o (Magma) [n^6*(n^4+1)/2: n in [0..30]]; // _Vincenzo Librandi_, Aug 29 2011
%o (PARI) a(n)=n^6*(n^4+1)/2 \\ _Charles R Greathouse IV_, Jul 26 2016
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_, Dec 11 2009