A393420 - OEIS

%I #9 Feb 24 2026 05:10:09

%S 1,8,124,2400,52016,1207808,29379840,739014144,19065460480,

%T 501694482432,13413481036800,363345251303424,9950454941564928,

%U 275038274134999040,7663078706655395840,214990114377881223168,6068314538667340136448,172205110768067713433600,4910172479006050281062400

%N Expansion of (1/x) * Series_Reversion( x * (4 * (1 - x)^2 - 3) ).

%F G.f. A(x) satisfies A(x) = 1/(4 * (1 - x*A(x))^2 - 3).

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

%F D-finite with recurrence 3*n*(n+1)*a(n) -46*n*(2*n-1)*a(n-1) -3*(3*n-2)*(3*n-4)*a(n-2)=0. - _R. J. Mathar_, Feb 24 2026

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serreverse(x*(4*(1-x)^2-3))/x)

%Y Cf. A006013, A393418, A393419, A393421.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Feb 14 2026