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%I #16 Sep 08 2022 08:45:49
%S 0,1,384,13122,163840,1171875,5878656,23059204,75497472,215233605,
%T 550000000,1286153286,2794881024,5710115047,11068417920,20503125000,
%U 36507222016,62781816969,104689625472,169835630410,268800000000,416051452971,631072545664
%N a(n) = n^8*(n + 1)/2.
%H G. C. Greubel, <a href="/A168675/b168675.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10,-45, 120,-210,252,-210,120,-45,10,-1).
%F From _Harvey P. Dale_, Dec 11 2011: (Start)
%F a(0)=0, a(1)=1, a(2)=384, a(3)=13122, a(4)=163840, a(5)=1171875, a(6)=5878656, a(7)=23059204, a(8)=75497472, a(9)=215233605, a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10).
%F G.f.: (x*(x*(x*(x*(x*(x*(x*(128*x + 5281) +38454) +78095) +49780) +9327) +374) + 1))/(1 - x)^10. (End)
%t Table[n^8(n+1)/2,{n,0,30}] (* _Harvey P. Dale_, Dec 11 2011 *)
%t LinearRecurrence[{10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {0, 1, 384, 13122, 163840, 1171875, 5878656, 23059204, 75497472, 215233605}, 20] (* _Vincenzo Librandi_, Jul 30 2016 *)
%o (Magma) [n^8*(n+1)/2: n in [0..30]]; // _Vincenzo Librandi_, Jul 30 2016
%o (PARI) a(n)=n^8*(n+1)/2 \\ _Charles R Greathouse IV_, Jul 30 2016
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_, Dec 11 2009
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