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 A373463 #27 May 25 2025 20:15:33
%S A373463 1,-5,15,-35,70,-124,190,-220,55,715,-2999,8585,-20580,43520,-81940,
%T A373463 134376,-176195,118435,279235,-1572395,4900626,-12339900,27139450,
%U A373463 -53163300,91745475,-131888749,125584845,66464465,-781173960,2736565920,-7295547624,16717081040
%N A373463 Expansion of 1/((1 + x)^5 - 2*x^5).
%H A373463 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (-5,-10,-10,-5,1).
%F A373463 a(n) = -5*a(n-1) - 10*a(n-2) - 10*a(n-3) - 5*a(n-4) + a(n-5).
%F A373463 a(n) = (-1)^n * Sum_{k=0..floor(n/5)} (-2)^k * binomial(n+4,5*k+4).
%t A373463 CoefficientList[Series[1/((1+x)^5-2x^5),{x,0,40}],x] (* or *) LinearRecurrence[{-5,-10,-10,-5,1},{1,-5,15,-35,70},40] (* _Harvey P. Dale_, May 25 2025 *)
%o A373463 (PARI) my(N=40, x='x+O('x^N)); Vec(1/((1+x)^5-2*x^5))
%Y A373463 Cf. A108369, A375163.
%Y A373463 Cf. A000750.
%K A373463 sign,easy
%O A373463 0,2
%A A373463 _Seiichi Manyama_, Aug 04 2024