%I #7 Oct 04 2024 14:19:25
%S 1,3,19,138,1072,8661,71758,605094,5169286,44605527,387969346,
%T 3396331158,29891385937,264264469542,2345319267553,20883723678234,
%U 186497307222706,1669724703219384,14983025158691938,134719748524295094,1213531265862339751
%N Expansion of 1/((1 - x^2)^3 - 9*x)^(1/3).
%F a(n) = Sum_{k=0..floor(n/2)} (-9)^(n-2*k) * binomial(-1/3,n-2*k) * binomial(3*n-5*k,k).
%o (PARI) my(N=30, x='x+O('x^N)); Vec(1/((1-x^2)^3-9*x)^(1/3))
%Y Cf. A376802, A376806.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Oct 04 2024