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.
%I A163277 #14 May 14 2022 03:54:38 %S A163277 0,2,576,17496,204800,1406250,6858432,26353376,84934656,239148450, %T A163277 605000000,1403076312,3027787776,6149354666,11859019200,21870000000, %U A163277 38788923392,66474865026,110505715776,178774347800,282240000000 %N A163277 a(n) = n^7*(n+1)^2/2. %H A163277 G. C. Greubel, <a href="/A163277/b163277.txt">Table of n, a(n) for n = 0..1000</a> %H A163277 <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 A163277 From _R. J. Mathar_, Feb 05 2010: (Start) %F A163277 a(n) = n^2*A163275(n). %F A163277 G.f.: 2*x*(1 +278*x +5913*x^2 +27760*x^3 +38435*x^4 +16434*x^5 +1867*x^6 +32*x^7)/(x-1)^10. (End) %F A163277 From _Amiram Eldar_, May 14 2022: (Start) %F A163277 Sum_{n>=1} 1/a(n) = 16 - 7*Pi^2/3 - 4*Pi^4/45 - 4*Pi^6/945 + 10*zeta(3) + 6*zeta(5) + 2*zeta(7). %F A163277 Sum_{n>=1} (-1)^(n+1)/a(n) = 28*log(2) + 15*zeta(3)/2 + 45*zeta(5)/8 + 63*zeta(7)/32 - 16 - 5*Pi^2/6 - 7*Pi^4/90 - 31*Pi^6/7560. (End) %p A163277 A163277 := proc(n) n^7*(n+1)^2/2 ; end proc: seq(A163277(n),n=0..60) ; \\ _R. J. Mathar_, Feb 05 2010 %t A163277 Table[(1/2)*n^7*(n + 1)^2, {n,0,50}] (* _G. C. Greubel_, Dec 12 2016 *) %o A163277 (PARI) concat([0], Vec(2*x*(1 +278*x +5913*x^2 +27760*x^3 +38435*x^4 +16434*x^5 +1867*x^6 +32*x^7)/(x-1)^10 + O(x^50))) \\ _G. C. Greubel_, Dec 12 2016 %o A163277 (Magma) [n^7*(n+1)^2/2: n in [0..30]]; // _Vincenzo Librandi_, Dec 13 2016 %Y A163277 Cf. A006002, A099903, A163102, A163274, A163275, A163276. %K A163277 easy,nonn %O A163277 0,2 %A A163277 _Omar E. Pol_, Jul 24 2009 %E A163277 Extended by _R. J. Mathar_, Feb 05 2010