This procedure finds the generating function of the hybrid terms that results from the term wise multiplication of the sequences encoded by the generating functions gf1, gf2, ....

The command with(genfunc,rgf_hybrid) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{genfunc}\right)\:$

$\mathrm{rgf\_hybrid}\left(z\,\frac{1}{1-2z}\,\frac{2z}{1-3z}\right)$

$-\frac{4z}{6z-1}$

$\mathrm{rgf\_hybrid}\left(z\,\frac{z}{1-z-z^2}\,\frac{1}{1-2z}\right)$

$-\frac{2z}{4z^2+2z-1}$

$\mathrm{pz}≔\mathrm{rgf\_encode}\left(n\,n\,z\right)$

$\mathrm{pz}≔\frac{z}{{\left(1-z\right)}^2}$

$\mathrm{fz}≔\mathrm{rgf\_hybrid}\left(z\,\mathrm{pz}\,\mathrm{pz}\right)$

$\mathrm{fz}≔-\frac{z^2+z}{z^3-3z^2+3z-1}$

$\mathrm{normal}\left(\mathrm{rgf\_expand}\left(\mathrm{fz}\,z\,n\right)\right)$

$n^2$