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