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 A375163 #17 Aug 05 2024 08:41:53
%S A375163 1,-7,28,-84,210,-462,924,-1714,2975,-4795,6888,-7616,1428,27132,
%T A375163 -116276,352632,-919303,2180101,-4815188,10010980,-19650050,36268478,
%U A375163 -62075384,95196038,-118778345,73332329,207719344,-1138579904,3670243032,-9852434200,23858720872
%N A375163 Expansion of 1/((1 + x)^7 - 2*x^7).
%H A375163 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (-7,-21,-35,-35,-21,-7,1).
%F A375163 a(n) = -7*a(n-1) - 21*a(n-2) - 35*a(n-3) - 35*a(n-4) - 21*a(n-5) - 7*a(n-6) + a(n-7).
%F A375163 a(n) = (-1)^n * Sum_{k=0..floor(n/7)} (-2)^k * binomial(n+6,7*k+6).
%o A375163 (PARI) my(N=40, x='x+O('x^N)); Vec(1/((1+x)^7-2*x^7))
%Y A375163 Cf. A108369, A373463.
%Y A375163 Cf. A049018.
%K A375163 sign,easy
%O A375163 0,2
%A A375163 _Seiichi Manyama_, Aug 05 2024