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%I #12 Sep 08 2022 08:45:49
%S 0,1,32800,21523725,2147485696,76293953125,1410554977056,
%T 16616465343625,140737488486400,926510094691641,5000000000500000,
%U 22974864932671861,92442129449011200,332708304594003325,1088976668908450336
%N a(n) = n^6*(n^10 + 1)/2.
%H Vincenzo Librandi, <a href="/A168634/b168634.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (17,-136,680,-2380,6188,-12376,19448,-24310,24310,-19448,12376,-6188,2380,-680,136,-17,1).
%F From _G. C. Greubel_, Jul 27 2016: (Start)
%F G.f.: x*(1 + 32783*x + 20966261*x^2 + 1786042491*x^3 + 42691621273*x^4 + 391057753399*x^5 + 1603741596869*x^6 + 3191399458923*x^7 + 3191399458923*x^8 + 1603741596869*x^9 + 391057753399*x^10 + 42691621273*x^11 + 1786042491*x^12 + 20966261*x^13 + 32783*x^14 + x^15)/(1 - x)^17.
%F E.g.f.: (1/2)*x*(2 + 32798*x + 7141776*x^2 + 171798966*x^3 + 1096190565*x^4 + 2734926559*x^5 + 3281882604*x^6 + 2141764053*x^7 + 820784250*x^8 + 193754990*x^9 + 28936908*x^10 + 2757118*x^11 + 165620*x^12 + 6020*x^13 + 120*x^14 + x^15). (End)
%t Table[n^6*(n^10 + 1)/2, {n,0,25}] (* _G. C. Greubel_, Jul 27 2016 *)
%o (Magma)[n^6*(n^10+1)/2: n in [0..30]]; // _Vincenzo Librandi_, Aug 29 2011
%o (PARI) a(n)=n^6*(n^10+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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