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 A362126 #10 Apr 09 2023 08:07:57
%S A362126 1,2,7,18,47,118,290,702,1677,3966,9300,21654,50116,115388,264475,
%T A362126 603792,1373621,3115222,7045205,15892794,35769390,80337144,180091131,
%U A362126 403002108,900370600,2008572044,4474586920,9955434456,22123162421,49107537598,108891513251
%N A362126 Expansion of 1/(1 - x*(1+x)^2)^2.
%H A362126 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,3,-2,-6,-4,-1).
%F A362126 a(n) = 2*a(n-1) + 3*a(n-2) - 2*a(n-3) - 6*a(n-4) - 4*a(n-5) - a(n-6) for n > 5.
%F A362126 a(n) = Sum_{k=0..n} (-1)^k * binomial(-2,k) * binomial(2*k,n-k) = Sum_{k=0..n} (k+1) * binomial(2*k,n-k).
%o A362126 (PARI) my(N=40, x='x+O('x^N)); Vec(1/(1-x*(1+x)^2)^2)
%Y A362126 Column k=2 of A362125.
%Y A362126 Cf. A002478, A362084.
%K A362126 nonn,easy
%O A362126 0,2
%A A362126 _Seiichi Manyama_, Apr 08 2023