A371393 - OEIS

%I #11 Mar 21 2024 09:20:02

%S 1,7,65,695,8081,99303,1268961,16694295,224617265,3076621127,

%T 42757939841,601443961207,8546453367505,122502619954855,

%U 1769134504184865,25716831677125335,375988660156913265,5525224188936386055,81565308431025658305,1209038650866275440695

%N Expansion of (1/x) * Series_Reversion( x * (1-x) / (1+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} 3^k * binomial(2*(n+1),k) * binomial(2*n-k,n-k).

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

%o (PARI) a(n) = sum(k=0, n, 3^k*binomial(2*(n+1), k)*binomial(2*n-k, n-k))/(n+1);

%Y Cf. A082298, A371394.

%Y Cf. A064087.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Mar 21 2024