%I #8 Sep 30 2023 13:09:14
%S 1,2,5,13,33,77,147,128,-726,-5870,-28918,-117501,-419748,-1330265,
%T -3631065,-7585458,-5021553,62555365,485450778,2473377984,10459876208,
%U 38765746168,126610935508,352046019398,725506704096,264040020875,-7980075940060,-58806846330257
%N Expansion of (1/x) * Series_Reversion( x*(1+x+x^3)/(1+x)^3 ).
%F a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} (-1)^k * binomial(n+k,k) * binomial(2*n-k+2,n-3*k).
%o (PARI) a(n) = sum(k=0, n\3, (-1)^k*binomial(n+k, k)*binomial(2*n-k+2, n-3*k))/(n+1);
%Y Cf. A366116, A366118, A366119.
%Y Cf. A366096.
%K sign
%O 0,2
%A _Seiichi Manyama_, Sep 29 2023