%I #12 Jan 24 2024 05:56:00

%S 1,3,14,77,464,2964,19717,135131,947549,6765642,49022225,359545750,

%T 2664127354,19913283809,149968276974,1136856855549,8668000962927,

%U 66428474900907,511414514214628,3953420853213504,30674783555852576,238808419235022293,1864869207177530320

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

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

%F a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(2*n+2,k) * binomial(3*n-k+3,n-2*k).

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

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

%Y Cf. A106228, A369479.

%Y Cf. A143927, A369478.

%Y Cf. A369440.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jan 23 2024