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%I #8 Sep 29 2023 10:04:34
%S 1,2,5,15,51,187,719,2858,11650,48438,204630,875867,3790172,16554305,
%T 72883035,323109570,1441152303,6462494515,29118219850,131761291852,
%U 598529262016,2728346941040,12476533435028,57220220120080,263125059775970,1212942573227309
%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)} binomial(n+k,k) * binomial(2*n-k+2,n-3*k).
%o (PARI) a(n) = sum(k=0, n\3, binomial(n+k, k)*binomial(2*n-k+2, n-3*k))/(n+1);
%Y Cf. A366071, A366095, A366097.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Sep 29 2023
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