A368934 - OEIS

%I #10 Jan 10 2024 07:59:06

%S 1,3,16,104,751,5789,46656,388377,3313304,28816513,254548840,

%T 2277498340,20596833817,187974816142,1729033498416,16012809644088,

%U 149186508912927,1397300099214753,13149137686976324,124262625068365924,1178796712807563025

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

%F a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(n+k,k) * binomial(4*n-k+2,n-2*k).

%o (PARI) a(n) = sum(k=0, n\2, binomial(n+k, k)*binomial(4*n-k+2, n-2*k))/(n+1);

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

%Y Cf. A001002, A046736, A236339.

%Y Cf. A368938.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jan 10 2024