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

%I #16 Mar 21 2024 09:19:07

%S 1,5,46,521,6574,88658,1250920,18236849,272544886,4153080950,

%T 64284022516,1007929418570,15974993572732,255522850658564,

%U 4119461259700060,66869059171095809,1091990982773631910,17927521032225339854,295717190725184361364,4898634803627227516238

%N Expansion of (1/x) * Series_Reversion( x * (1-3*x)^2 / (1-x) ).

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

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

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-3*x)^2/(1-x))/x)

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

%Y Cf. A107841, A371385.

%Y Cf. A371362.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Mar 20 2024