A371369 - OEIS

%I #10 Mar 20 2024 09:39:48

%S 1,9,161,3593,89729,2399817,67222433,1946874569,57824172545,

%T 1751650872713,53910484818849,1680961253003401,52987626458710657,

%U 1685806021244435913,54062032254640697505,1745723303156237416265,56713604222408801019905

%N Expansion of (1/x) * Series_Reversion( x * (1-8*x)^2 / (1-7*x) ).

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

%F a(n) = (1/(n+1)) * Sum_{k=0..n} 7^(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*(1-8*x)^2/(1-7*x))/x)

%o (PARI) a(n) = sum(k=0, n, 7^(n-k)*binomial(2*n+k+1, k)*binomial(2*n, n-k))/(n+1);

%Y Cf. A082147.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Mar 19 2024