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%I #23 Sep 08 2022 08:45:48
%S 0,1,258,9846,131080,976575,5038866,20176828,67108896,193710285,
%T 500000050,1178973906,2579890248,5302249771,10330523490,19221679800,
%U 34359738496,59293938393,99179645346,161343849070,256000000200,397140023511,603634609138,900576330996
%N a(n) = n^2*(n^7+1)/2.
%H G. C. Greubel, <a href="/A168125/b168125.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_, Jan 31 2012: (Start)
%F 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), where
%F a(0)=0, a(1)=1, a(2)=258, a(3)=9846, a(4)=131080, a(5)=976575, a(6)=5038866, a(7)=20176828, a(8)=67108896, a(9)=193710285. (End)
%F G.f.: x*(1 + 248*x+ 7311*x^2 + 44110*x^3 + 78095*x^4 + 44124*x^5 + 7297*x^6 + 254*x^7)/(1 - x)^10. - _Ilya Gutkovskiy_, Jul 14 2016
%t Table[(n^2 (n^7+1))/2, {n,0,20}] (* or *) LinearRecurrence[ {10,-45,120, -210,252,-210,120,-45,10, -1}, {0,1,258, 9846,131080,976575, 5038866, 20176828,67108896,193710285},21] (* _Harvey P. Dale_, Jan 31 2012 *)
%t CoefficientList[Series[x (1 + 248 x + 7311 x^2 + 44110 x^3 + 78095 x^4 + 44124 x^5 + 7297 x^6 + 254 x^7)/(1-x)^10, {x, 0, 33}], x] (* _Vincenzo Librandi_, Jul 14 2016 *)
%o (Magma) [n^2*(n^7+1)/2: n in [0..25]]; // _Vincenzo Librandi_, Jul 14 2016
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Dec 11 2009
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