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%I #11 Apr 30 2024 06:09:31
%S 1,1,3,16,75,336,1536,7155,33627,158974,755508,3606648,17281776,
%T 83068766,400368741,1934204661,9363509531,45411373098,220593832062,
%U 1073127878085,5227288727580,25492636911240,124457166046832,608207193661734,2974913417047440
%N Coefficient of x^n in the expansion of ( (1-x+x^3)^2 / (1-x)^3 )^n.
%F a(n) = Sum_{k=0..floor(n/3)} binomial(2*n,k) * binomial(2*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)^3 / (1-x+x^3)^2 ). See A369231.
%o (PARI) a(n, s=3, t=2, u=3) = sum(k=0, n\s, binomial(t*n, k)*binomial((u-t+1)*n-(s-1)*k-1, n-s*k));
%Y Cf. A369231, A372416.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Apr 29 2024
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