A369509 - OEIS

%I #9 Jan 25 2024 07:50:25

%S 1,6,61,756,10406,152880,2348164,37250298,605592377,10036783746,

%T 168947499695,2880456168330,49638925087101,863251245610368,

%U 15130529347412496,267011151724625220,4740245924729076390,84599747038748783220,1516992745930706932654

%N Expansion of (1/x) * Series_Reversion( x * ((1-x)^2-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} binomial(2*n+k+1,k) * binomial(5*n+k+3,n-k).

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serreverse(x*((1-x)^2-x)^2)/x)

%o (PARI) a(n) = sum(k=0, n, binomial(2*n+k+1, k)*binomial(5*n+k+3, n-k))/(n+1);

%Y Cf. A369510, A369511.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jan 25 2024