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%I #10 Apr 29 2024 09:06:36
%S 1,1,1,4,13,31,91,313,988,3095,10377,35146,117682,400117,1381582,
%T 4779997,16599766,58095076,204319835,720756820,2552544940,9074710255,
%U 32356325145,115679362789,414701335849,1490297002000,5367227015647,19369656905210,70038419041844
%N Expansion of (1/x) * Series_Reversion( x * (1+x)^2 / (1+x+x^3)^3 ).
%H <a href="/index/Res#revert">Index entries for reversions of series</a>
%F a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(3*n+3,k) * binomial(n-k+1,n-3*k).
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1+x)^2/(1+x+x^3)^3)/x)
%o (PARI) a(n, s=3, t=3, u=-2) = sum(k=0, n\s, binomial(t*(n+1), k)*binomial((t+u)*(n+1)-k, n-s*k))/(n+1);
%Y Cf. A372376, A372378.
%K nonn
%O 0,4
%A _Seiichi Manyama_, Apr 29 2024
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