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%I #6 May 02 2024 09:46:21
%S 1,4,36,370,4012,44814,510198,5886206,68579020,805045276,9507007686,
%T 112817021332,1344160003030,16069300956726,192662610805386,
%U 2315694030560640,27893938099222316,336643301659031102,4069747367955175236,49274614400855690158
%N Coefficient of x^n in the expansion of 1 / ( (1-x) * (1-x-x^3) )^(2*n).
%F a(n) = Sum_{k=0..floor(n/3)} binomial(2*n+k-1,k) * binomial(5*n-2*k-1,n-3*k).
%F The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x * (1-x)^2 * (1-x-x^3)^2 ). See A368968.
%o (PARI) a(n, s=3, t=2, u=2) = sum(k=0, n\s, binomial(t*n+k-1, k)*binomial((t+u+1)*n-(s-1)*k-1, n-s*k));
%Y Cf. A368968, A372465.
%K nonn
%O 0,2
%A _Seiichi Manyama_, May 01 2024
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