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%I #12 Sep 08 2022 08:45:49
%S 0,1,16416,7174818,536872960,15258796875,235092515616,2373780813796,
%T 17592186175488,102945566313045,500000000500000,2088624085593606,
%U 7703510788786176,25592946509458783,77784047782670880
%N a(n) = n^6*(n^9 + 1)/2.
%H Vincenzo Librandi, <a href="/A168633/b168633.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1).
%F From _G. C. Greubel_, Jul 27 2016: (Start)
%F G.f.: x*(1 + 16400*x + 6912282*x^2 + 424045232*x^3 + 7520616535*x^4 + 51388495488*x^5 + 155693803020*x^6 + 223769408736*x^7 + 155693795391*x^8 + 51388503440*x^9 + 7520612986*x^10 + 424045680*x^11 + 6912457*x^12 + 16352*x^13)/(1 - x)^16.
%F E.g.f.: (1/2)*x*(2 + 16414*x + 2375191*x^2 + 42356015*x^3 + 210766935*x^4 + 420693274*x^5 + 408741333*x^6 + 216627840*x^7 + 67128490*x^8 + 12662650*x^9 + 1479478*x^10 + 106470*x^11 + 4550*x^12 + 105*x^13 + x^14). (End)
%t Table[n^6*(n^9 + 1)/2, {n,0,25}] (* _G. C. Greubel_, Jul 27 2016 *)
%o (Magma) [n^6*(n^9+1)/2: n in [0..30]]; // _Vincenzo Librandi_, Aug 29 2011
%o (PARI) a(n)=n^6*(n^9+1)/2 \\ _Charles R Greathouse IV_, Jul 28 2016
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_, Dec 11 2009
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