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 A369505 Expansion of (1/x) * Series_Reversion( x / ((1+x)^3+x)^2 ). 1

%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

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Last modified September 15 01:49 EDT 2024. Contains 375929 sequences. (Running on oeis4.)