The function inverse(p) returns a formal power series that is the inverse of p with respect to multiply.

That is, multiply(p, inverse(p)) will return the formal power series equivalent to 1.

The command with(powseries,inverse) allows the use of the abbreviated form of this command.

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

$\mathrm{powcreate}\left(t\left(n\right)=\frac{t\left(n-1\right)}{n}\,t\left(0\right)=1\right)\:$

$s≔\mathrm{inverse}\left(t\right)\:$

$\mathrm{tpsform}\left(s\,x\,7\right)$

$1-x+\frac{1}{2}{x}^2-\frac{1}{6}{x}^3+\frac{1}{24}{x}^4-\frac{1}{120}{x}^5+\frac{1}{720}{x}^6+O\left(x^7\right)$