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%I #16 Jan 13 2024 10:45:09
%S 1,2,9,48,286,1820,12116,83334,587537,4223582,30840355,228111390,
%T 1705509981,12868775056,97867753424,749401318160,5772939358590,
%U 44708058004740,347879528717526,2718400037837988,21323471768334120,167844335760482220,1325332432687278960
%N Expansion of (1/x) * Series_Reversion( x * (1-x-x^2)^2 ).
%H Seiichi Manyama, <a href="/A368961/b368961.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Res#revert">Index entries for reversions of series</a>
%F a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(2*n+k+1,k) * binomial(3*n-k+1,n-2*k).
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x-x^2)^2)/x)
%o (PARI) a(n, s=2, t=2, u=0) = sum(k=0, n\s, binomial(t*(n+1)+k-1, k)*binomial((t+u+1)*(n+1)-(s-1)*k-2, n-s*k))/(n+1);
%Y Cf. A368965, A368967.
%Y Cf. A001002.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Jan 10 2024
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