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.

A168662 a(n) = n^7*(n^5 + 1)/2.

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%I A168662 #23 Mar 24 2025 12:54:04
%S A168662 0,1,2112,266814,8396800,122109375,1088531136,6921055372,34360786944,
%T A168662 141217159725,500005000000,1569223931946,4458068140032,11649073935499,
%U A168662 28347008894400,64873254375000,140737622573056,291311323784217,578415996823104,1106657906468950,2048000640000000
%N A168662 a(n) = n^7*(n^5 + 1)/2.
%H A168662 Vincenzo Librandi, <a href="/A168662/b168662.txt">Table of n, a(n) for n = 0..10000</a>
%H A168662 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).
%F A168662 From _G. C. Greubel_, Jul 28 2016: (Start)
%F A168662 G.f.: x*(1 + 2099*x + 239436*x^2 + 5092668*x^3 + 33159150*x^4 + 81259650*x^5 + 81252636*x^6 + 33159324*x^7 + 5095017*x^8 + 238835*x^9 + 1984*x^10)/(1-x)^13.
%F A168662 E.g.f.: (1/2)*x*(2 + 2110*x + 86827*x^2 + 611851*x^3 + 1379540*x^4 + 1323673*x^5 + 627397*x^6 + 159027*x^7 + 22275*x^8 + 1705*x^9 + 66*x^10 + x^11)*exp(x). (End)
%t A168662 Table[n^7 (n^5+1)/2,{n,0,20}] (* _Harvey P. Dale_, May 17 2016 *)
%o A168662 (Magma) [n^7*(n^5+1)/2: n in [0..20]]; // _Vincenzo Librandi_, Aug 28 2011
%o A168662 (PARI) a(n)=n^7*(n^5+1)/2 \\ _Charles R Greathouse IV_, Jul 29 2016
%o A168662 (SageMath)
%o A168662 def A168662(n): return n^2*binomial(n^5+1,2)
%o A168662 print([A168662(n) for n in range(31)]) # _G. C. Greubel_, Mar 24 2025
%Y A168662 Cf. A168635.
%K A168662 nonn,easy
%O A168662 0,3
%A A168662 _N. J. A. Sloane_, Dec 11 2009