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 A375292 #10 Aug 10 2024 11:03:14
%S A375292 1,1,1,0,-3,-8,-14,-15,1,51,146,261,286,-24,-1029,-2975,-5375,-5930,
%T A375292 591,22014,63886,115947,128183,-14595,-486466,-1413161,-2569868,
%U A375292 -2840890,361667,10972167,31861581,57980426,64018181,-8985428,-250991300,-727998021,-1324662165
%N A375292 Expansion of 1/sqrt((1 - x + x^3)^2 + 4*x^4).
%F A375292 n*a(n) = (2*n-1)*a(n-1) - (n-1)*a(n-2) - (2*n-3)*a(n-3) - 2*(n-2)*a(n-4) - (n-3)*a(n-6).
%F A375292 a(n) = Sum_{k=0..floor(n/3)} (-1)^k * binomial(n-2*k,k)^2.
%o A375292 (PARI) my(N=40, x='x+O('x^N)); Vec(1/sqrt((1-x+x^3)^2+4*x^4))
%o A375292 (PARI) a(n) = sum(k=0, n\3, (-1)^k*binomial(n-2*k, k)^2);
%Y A375292 Cf. A375021, A375293.
%Y A375292 Cf. A246840.
%K A375292 sign
%O A375292 0,5
%A A375292 _Seiichi Manyama_, Aug 10 2024