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Expansion of (1/x) * Series_Reversion( x * (1-x-x^4/(1-x)^3) ).
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%I #12 Jan 26 2024 11:10:20

%S 1,1,2,5,15,52,198,793,3255,13529,56696,239340,1017900,4361840,

%T 18828606,81833505,357865215,1573549667,6952392450,30848928525,

%U 137403484655,614104910096,2753200345000,12378494389660,55799811151140,252141767612812,1141894552992368

%N Expansion of (1/x) * Series_Reversion( x * (1-x-x^4/(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/4)} binomial(n+k,k) * binomial(2*n,n-4*k).

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x-x^4/(1-x)^3))/x)

%o (PARI) a(n) = sum(k=0, n\4, binomial(n+k, k)*binomial(2*n, n-4*k))/(n+1);

%Y Cf. A063021, A367317, A367414.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Jan 26 2024