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%I #14 May 02 2024 09:49:22
%S 1,2,16,119,948,7732,64231,540311,4588076,39244106,337624066,
%T 2918384229,25325306031,220497804256,1925231880973,16850975055139,
%U 147807248526268,1298926641563548,11434042768577866,100800817171002817,889839745865544598
%N Coefficient of x^n in the expansion of ( (1-x) / (1-x-x^2)^3 )^n.
%F a(n) = Sum_{k=0..floor(n/2)} binomial(3*n+k-1,k) * binomial(3*n-k-1,n-2*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-x^2)^3 / (1-x) ). See A369487.
%t a[n_]:=SeriesCoefficient[((1-x)/(1-x-x^2)^3)^n,{x,0,n}]; Array[a,21,0] (* _Stefano Spezia_, May 01 2024 *)
%o (PARI) a(n, s=2, t=3, u=1) = 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. A370620, A370622, A370623.
%Y Cf. A369487.
%K nonn
%O 0,2
%A _Seiichi Manyama_, May 01 2024
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