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 A375255 #18 Aug 09 2024 10:07:42
%S A375255 1,2,1,-6,-20,-26,19,162,339,180,-1000,-3380,-4459,3042,27221,57614,
%T A375255 31940,-166446,-571161,-764478,485479,4573160,9790000,5654040,
%U A375255 -27693719,-96502718,-131022359,77196834,768159900,1663276734,998702459,-4605941918,-16302704581
%N A375255 Expansion of 1/(1 - 2*x + 3*x^2 + 2*x^3 + x^4).
%H A375255 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,-3,-2,-1).
%F A375255 a(n) = 2*a(n-1) - 3*a(n-2) - 2*a(n-3) - a(n-4).
%F A375255 a(n) = (1/2) * Sum_{k=0..floor(n/2)} (-1)^k * binomial(2*n-2*k+2,2*k+1).
%o A375255 (PARI) my(N=40, x='x+O('x^N)); Vec(1/(1-2*x+3*x^2+2*x^3+x^4))
%o A375255 (PARI) a(n) = sum(k=0, n\2, (-1)^k*binomial(2*n-2*k+2, 2*k+1))/2;
%Y A375255 Cf. A182890, A375273.
%Y A375255 Cf. A375021, A375275.
%K A375255 sign
%O A375255 0,2
%A A375255 _Seiichi Manyama_, Aug 09 2024