A371387 - OEIS

%I #8 Mar 21 2024 09:19:34

%S 1,11,205,4647,116873,3135635,87924597,2545845135,75534363601,

%T 2284439539035,70166186106333,2182759455876663,68630655620066265,

%U 2177561996773904483,69632831106680348165,2241852665024904670239,72608750028928583936673

%N Expansion of (1/x) * Series_Reversion( x * (1-4*x)^3 / (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} 3^k * binomial(3*n+k+2,k) * binomial(3*n+1,n-k).

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serreverse(x*(1-4*x)^3/(1-x))/x)

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

%Y Cf. A131763, A371386.

%Y Cf. A371365.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Mar 20 2024