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The function multconst(p, const) returns the formal power series where each coefficient is const times the corresponding coefficient in p.

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

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

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

$s≔\mathrm{multconst}\left(t\,-42\right)\:$

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

$\mathrm{-42}-42x-21x^2-7x^3-\frac{7}{4}{x}^4-\frac{7}{20}{x}^5+O\left(x^6\right)$