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Expansion of (1/x) * Series_Reversion( x * (1-7*x)^2 / (1-6*x) ).
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%I #11 Mar 20 2024 09:39:44

%S 1,8,127,2514,55679,1320530,32800020,842314362,22182639823,

%T 595816941756,16259068712391,449504473152288,12563255467347012,

%U 354392729335581224,10076681024065204760,288500953324319325402,8310071739586606559151

%N Expansion of (1/x) * Series_Reversion( x * (1-7*x)^2 / (1-6*x) ).

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

%F a(n) = (1/(n+1)) * Sum_{k=0..n} 6^(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*(1-7*x)^2/(1-6*x))/x)

%o (PARI) a(n) = sum(k=0, n, 6^(n-k)*binomial(2*n+k+1, k)*binomial(2*n, n-k))/(n+1);

%Y Cf. A081178.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Mar 19 2024