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%I #7 Sep 27 2023 10:07:35
%S 1,2,8,39,211,1218,7349,45790,292361,1902834,12577737,84205212,
%T 569788192,3890728052,26775751320,185525538183,1293171205833,
%U 9061500578178,63794947215218,451028012126797,3200898741338041,22794860112273294,162841330273522907
%N Expansion of (1/x) * Series_Reversion( x*(1-x)^3/(1-x+x^2) ).
%F a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(n+1,k) * binomial(3*n-k+1,n-2*k).
%o (PARI) a(n) = sum(k=0, n\2, binomial(n+1, k)*binomial(3*n-k+1, n-2*k))/(n+1);
%Y Cf. A005043, A109081, A366050.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Sep 27 2023
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