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A168526 a(n) = n^6*(n + 1)/2.

%I A168526 #21 Mar 20 2025 04:35:36
%S A168526 0,1,96,1458,10240,46875,163296,470596,1179648,2657205,5500000,
%T A168526 10629366,19408896,33787663,56471520,91125000,142606336,217238121,
%U A168526 323116128,470458810,672000000,943427331,1303868896,1776430668,2388787200,3173828125,4170362976
%N A168526 a(n) = n^6*(n + 1)/2.
%H A168526 Vincenzo Librandi, <a href="/A168526/b168526.txt">Table of n, a(n) for n = 0..1000</a>
%H A168526 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-1).
%F A168526 From _R. J. Mathar_, Dec 16 2009: (Start)
%F A168526 a(n) = 8*a(n-1) -28*a(n-2) +56*a(n-3) -70*a(n-4) +56*a(n-5) -28*a(n-6) +8*a(n-7) -a(n-8).
%F A168526 G.f.: x*(1 + 88*x + 718*x^2 + 1208*x^3 + 473*x^4 + 32*x^5)/(1-x)^8. (End)
%F A168526 E.g.f.: (1/2)*x*(2 + 94*x + 391*x^2 + 415*x^3 + 155*x^4 + 22*x^5 + x^6)*exp(x). - _G. C. Greubel_, Mar 20 2025
%t A168526 Table[n^6*(n+1)/2, {n,0,40}] (* _G. C. Greubel_, Jul 25 2016 *)
%o A168526 (Magma) [n^6*(n+1)/2: n in [0..30]]; // _Vincenzo Librandi_, Jul 25 2016
%o A168526 (SageMath)
%o A168526 def A168526(n): return n^5*binomial(n+1,2)
%o A168526 print([A168526(n) for n in range(41)]) # _G. C. Greubel_, Mar 20 2025
%Y A168526 Cf. A168029.
%K A168526 nonn,easy
%O A168526 0,3
%A A168526 _N. J. A. Sloane_, Dec 11 2009