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Expansion of (1/x) * Series_Reversion( x * (1-6*x)^2 / (1-5*x) ).
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%I #11 Mar 20 2024 09:39:40

%S 1,7,97,1675,32353,669103,14491441,324479203,7450571905,174479758615,

%T 4151241723265,100060420474555,2438221991122657,59964761207220415,

%U 1486507438771416529,37105090783548992659,931807879987468872193,23525616974931980536615

%N Expansion of (1/x) * Series_Reversion( x * (1-6*x)^2 / (1-5*x) ).

%H <a href="/index/Res#revert">Index entries for reversions of series</a>

%F a(n) = (1/(n+1)) * Sum_{k=0..n} 5^(n-k) * binomial(2*n+k+1,k) * binomial(2*n,n-k).

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serreverse(x*(1-6*x)^2/(1-5*x))/x)

%o (PARI) a(n) = sum(k=0, n, 5^(n-k)*binomial(2*n+k+1, k)*binomial(2*n, n-k))/(n+1);

%Y Cf. A078018.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Mar 19 2024