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 A375373 #18 Dec 11 2024 13:07:04
%S A375373 1,-2,4,-4,6,-4,9,-4,16,0,28,16,57,58,132,172,322,476,817,1272,2112,
%T A375373 3360,5496,8832,14353,23158,37540,60668,98238,158876,257145,415988,
%U A375373 673168,1089120,1762324,2851408,4613769,7465138,12078948,19544044,31623034,51167036
%N A375373 Expansion of 1/( (1 + x)^2 * (1 - x^2*(1 + x)^2) ).
%H A375373 Harvey P. Dale, <a href="/A375373/b375373.txt">Table of n, a(n) for n = 0..1000</a>
%H A375373 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (-2,0,4,6,4,1).
%F A375373 a(n) = -2*a(n-1) + 4*a(n-3) + 6*a(n-4) + 4*a(n-5) + a(n-6).
%F A375373 a(n) = Sum_{k=0..floor(n/2)} binomial(2*k-2,n-2*k).
%F A375373 2*a(n) = 2*(-1)^n*(n+1) +A212804(n)-A057078(n). - _R. J. Mathar_, Aug 14 2024
%t A375373 CoefficientList[Series[1/((1+x)^2(1-x^2(1+x)^2)),{x,0,50}],x] (* or *) LinearRecurrence[{-2,0,4,6,4,1},{1,-2,4,-4,6,-4},50] (* _Harvey P. Dale_, Dec 11 2024 *)
%o A375373 (PARI) my(N=50, x='x+O('x^N)); Vec(1/((1+x)^2*(1-x^2*(1+x)^2)))
%o A375373 (PARI) a(n) = sum(k=0, n\2, binomial(2*k-2, n-2*k));
%Y A375373 Cf. A093040, A375372.
%K A375373 sign
%O A375373 0,2
%A A375373 _Seiichi Manyama_, Aug 13 2024