(PARI) {
A322220(n, k) = my(Sx=x, Sy=y, Cx=1, Cy=1); for(i=1, 2*n,
Sx = intformal( Cx*Cy +x*O(x^(2*n)), x);
Cx = 1 + intformal( Sx*Cy, x);
Sy = intformal( Cy*Cx +y*O(y^(2*k)), y);
Cy = 1 + intformal( Sy*Cx, y));
(2*n+1-2*k)!*(2*k)! *polcoeff(polcoeff(Sx, 2*n+1-2*k, x), 2*k, y)}
for(n=0, 20, print1(a(n), ", "))