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%I #8 Jan 13 2024 10:47:54
%S 1,0,-3,-3,21,54,-157,-828,816,11684,5352,-151407,-288759,1737498,
%T 6671607,-15789371,-122051205,58021488,1935857500,1977087345,
%U -26913144267,-70826569596,314853424458,1586212109946,-2594198888498,-29124507344868,-2575010176581
%N Expansion of (1/x) * Series_Reversion( x * (1+x^2/(1-x))^3 ).
%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)} (-1)^k * binomial(3*n+k+2,k) * binomial(n-k-1,n-2*k).
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1+x^2/(1-x))^3)/x)
%o (PARI) a(n, s=2, t=3, u=-3) = 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. A179848, A369081.
%Y Cf. A369013.
%K sign
%O 0,3
%A _Seiichi Manyama_, Jan 12 2024
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