cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A168527 a(n) = n^6*(n^2 + 1)/2.

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%I A168527 #20 Mar 20 2025 04:35:32
%S A168527 0,1,160,3645,34816,203125,863136,2941225,8519680,21789081,50500000,
%T A168527 108065221,216483840,410278765,741659296,1287140625,2155872256,
%U A168527 3499947505,5526986400,8515304461,12832000000,18954312741,27494626720,39229510585,55133208576
%N A168527 a(n) = n^6*(n^2 + 1)/2.
%H A168527 G. C. Greubel, <a href="/A168527/b168527.txt">Table of n, a(n) for n = 0..1000</a>
%H A168527 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).
%F A168527 G.f.: (x + 151*x^2 + 2241*x^3 + 7687*x^4 + 7687*x^5 + 2241*x^6 + 151*x^7 + x^8)/(1 - x)^9. - _G. C. Greubel_, Jul 25 2016
%F A168527 E.g.f.: (1/2)*x*(2 + 158*x + 1056*x^2 + 1766*x^3 + 1065*x^4 + 267*x^5 + 28*x^6 + x^7)*exp(x). - _G. C. Greubel_, Mar 20 2025
%t A168527 Table[n^6*(n^2+1)/2, {n,0,40}] (* _G. C. Greubel_, Jul 25 2016 *)
%t A168527 LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1}, {0,1,160,3645,34816,203125, 863136,2941225,8519680}, 30] (* _Harvey P. Dale_, May 10 2018 *)
%o A168527 (Magma) [n^6*(n^2 + 1)/2: n in [0..30]]; // _Vincenzo Librandi_, Jul 25 2016
%o A168527 (SageMath)
%o A168527 def A168527(n): return n^4*binomial(n^2+1,2)
%o A168527 print([A168527(n) for n in range(41)]) # _G. C. Greubel_, Mar 20 2025
%Y A168527 Cf. A168526.
%K A168527 nonn
%O A168527 0,3
%A A168527 _N. J. A. Sloane_, Dec 11 2009