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 A375273 #11 Aug 09 2024 10:07:37
%S A375273 1,2,7,24,73,238,763,2436,7821,25050,80255,257200,824081,2640582,
%T A375273 8461187,27111644,86872853,278363058,891946503,2858027016,9157854361,
%U A375273 29344123550,94026132235,301283944500,965391362461,3093362593162,9911930522767,31760378496864
%N A375273 Expansion of 1/(1 - 2*x - 3*x^2 - 4*x^3 + 4*x^4).
%H A375273 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,3,4,-4).
%F A375273 a(n) = 2*a(n-1) + 3*a(n-2) + 4*a(n-3) - 4*a(n-4).
%F A375273 a(n) = (1/2) * Sum_{k=0..floor(n/2)} 2^k * binomial(2*n-2*k+2,2*k+1).
%o A375273 (PARI) my(N=30, x='x+O('x^N)); Vec(1/(1-2*x-3*x^2-4*x^3+4*x^4))
%o A375273 (PARI) a(n) = sum(k=0, n\2, 2^k*binomial(2*n-2*k+2, 2*k+1))/2;
%Y A375273 Cf. A182890, A375255.
%Y A375273 Cf. A108480, A108488.
%K A375273 nonn
%O A375273 0,2
%A A375273 _Seiichi Manyama_, Aug 09 2024