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%I #20 Jan 14 2024 08:53:57
%S 1,0,0,2,2,2,17,36,59,240,669,1452,4538,13574,34505,99816,299112,
%T 825768,2364715,7023466,20182611,58327250,172491553,505163444,
%U 1476966513,4370772096,12924382671,38149522136,113266357609,336894290910,1001473479313,2985508193930
%N Expansion of (1/x) * Series_Reversion( x * (1-x^3/(1-x))^2 ).
%H Seiichi Manyama, <a href="/A369011/b369011.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/3)} binomial(2*n+k+1,k) * binomial(n-2*k-1,n-3*k).
%o (PARI) my(N=40, x='x+O('x^N)); Vec(serreverse(x*(1-x^3/(1-x))^2)/x)
%o (PARI) a(n, s=3, t=2, u=-2) = 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. A211789, A368957.
%Y Cf. A054514, A369014.
%Y Cf. A368962, A368966, A368968.
%K nonn
%O 0,4
%A _Seiichi Manyama_, Jan 11 2024