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%I #11 Apr 30 2024 06:08:59
%S 1,2,10,59,366,2332,15121,99276,657894,4391438,29482320,198865680,
%T 1346655921,9149295482,62336961732,425760311734,2914151872614,
%U 19983724103726,137267022656710,944287970305935,6504676822047876,44861522295224400,309742638630690264
%N Coefficient of x^n in the expansion of ( (1-x+x^3) / (1-x)^3 )^n.
%F a(n) = Sum_{k=0..floor(n/3)} binomial(n,k) * binomial(3*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) ). See A366052.
%o (PARI) a(n, s=3, t=1, 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. A372413, A372414.
%Y Cf. A366052.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Apr 29 2024
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