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genfunc

 rgf_term
 finds values of terms in a sequence

 Calling Sequence rgf_term(Fz, z, n)

Parameters

 Fz - rational generating function of z z - name, generating function variable n - integer, index of term to evaluate

Description

 • This procedure finds the value of the nth term in the sequence encoded by the generating function Fz.
 • The value FAIL is returned if Fz is a trivial rational generating function.
 • The command with(genfunc,rgf_term) allows the use of the abbreviated form of this command.

Examples

 > $\mathrm{with}\left(\mathrm{genfunc}\right):$
 > $\mathrm{rgf_term}\left(\frac{1}{1-2z},z,100\right)$
 ${1267650600228229401496703205376}$ (1)
 > $\mathrm{rgf_term}\left(\frac{z}{{\left(1-z\right)}^{2}},z,1001\right)$
 ${1001}$ (2)
 > $\mathrm{rgf_term}\left(\frac{1}{1-az},z,26\right)$
 ${{a}}^{{26}}$ (3)
 > $\mathrm{rgf_term}\left(\frac{1}{1-y-yz},z,58\right)$
 ${-}\frac{{{y}}^{{58}}}{{\left({y}{-}{1}\right)}^{{59}}}$ (4)