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%I #11 Jan 13 2024 10:47:59
%S 1,0,0,-2,-2,-2,13,32,55,-72,-439,-1152,-506,4870,20613,31744,-26392,
%T -313096,-826529,-654362,3635175,16431826,30100349,-15474300,
%U -262654439,-780688624,-756130333,3013376172,15711713509,31584466782,-6090973971,-250819494954
%N Expansion of (1/x) * Series_Reversion( x * (1+x^3/(1-x))^2 ).
%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)} (-1)^k * 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, (-1)^k*binomial(t*(n+1)+k-1, k)*binomial((t+u+1)*(n+1)-(s-1)*k-2, n-s*k))/(n+1);
%Y Cf. A168491, A369076.
%Y Cf. A368970, A368974, A368976.
%Y Cf. A369011.
%K sign
%O 0,4
%A _Seiichi Manyama_, Jan 12 2024
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