%I #9 Mar 03 2024 09:52:52
%S 1,1,2,4,8,14,15,-30,-297,-1442,-5693,-20046,-64765,-192911,-522954,
%T -1236717,-2221422,-848673,18142403,122417208,573446212,2287694033,
%U 8211900486,26984131280,81027339912,217474121511,487508197964,690838844798,-1034716617740
%N Expansion of (1/x) * Series_Reversion( x * (1/(1-x^3) - x) ).
%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)} (-1)^k * binomial(2*n-3*k+1,k) * binomial(2*n-3*k,n-3*k).
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1/(1-x^3)-x))/x)
%o (PARI) a(n) = sum(k=0, n\3, (-1)^k*binomial(2*n-3*k+1, k)*binomial(2*n-3*k, n-3*k))/(n+1);
%Y Cf. A370839, A370841.
%Y Cf. A369630.
%K sign
%O 0,3
%A _Seiichi Manyama_, Mar 03 2024
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