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%I #13 Apr 30 2024 06:07:42
%S 1,0,6,9,78,225,1293,4851,24174,101583,480531,2123913,9869973,
%T 44669742,206614827,946394109,4378019310,20189406771,93556141449,
%U 433284753414,2011960692003,9345929458455,43484293732413,202453490369727,943647920498997,4401470801019600
%N Coefficient of x^n in the expansion of ( (1-x+x^2) / (1-x) )^(3*n).
%F a(n) = Sum_{k=0..floor(n/2)} binomial(3*n,k) * binomial(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)^3 / (1-x+x^2)^3 ). See A369230.
%o (PARI) a(n, s=2, t=3, 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. A372410, A372411.
%Y Cf. A369230.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Apr 29 2024
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