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%I #8 Jan 25 2024 07:49:59
%S 1,8,86,1066,14361,204314,3020745,45955442,714723588,11312450432,
%T 181625888244,2950848879096,48423670556100,801454908292020,
%U 13363137183238881,224253208102065664,3784736105491395780,64197997357038408976,1093863031541592651003
%N Expansion of (1/x) * Series_Reversion( x / ((1+x)^3+x)^2 ).
%H <a href="/index/Res#revert">Index entries for reversions of series</a>
%F a(n) = (1/(n+1)) * Sum_{k=0..n} binomial(2*n+2,k) * binomial(6*n-3*k+6,n-k).
%o (PARI) my(N=20, x='x+O('x^N)); Vec(serreverse(x/((1+x)^3+x)^2)/x)
%o (PARI) a(n) = sum(k=0, n, binomial(2*n+2, k)*binomial(6*n-3*k+6, n-k))/(n+1);
%Y Cf. A003645, A369502.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Jan 25 2024