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%I #9 Sep 27 2023 10:06:10
%S 1,-1,1,0,-3,9,-16,13,29,-157,391,-562,-32,3002,-10373,20747,-18083,
%T -47941,271117,-712216,1066699,122131,-6464446,22907125,-46951992,
%U 40883304,120187926,-679375906,1809757015,-2731745887,-468147579,17768126376,-63256877763
%N Expansion of (1/x) * Series_Reversion( x/(1-x+x^3) ).
%F a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} (-1)^(n-k) * binomial(n+1,k) * binomial(n-k+1,n-3*k).
%o (PARI) a(n) = sum(k=0, n\3, (-1)^(n-k)*binomial(n+1, k)*binomial(n-k+1, n-3*k))/(n+1);
%Y Cf. A049128, A114997, A366052, A366053.
%Y Cf. A071879.
%K sign
%O 0,5
%A _Seiichi Manyama_, Sep 27 2023