Ordinary generating function

A sequence $a_n$ Coefficients as polynomials

$g(x)=a_0+a_{1}x+a_2{x}^2\dots a_n{x}^n(-1<x<1)$

The value range of x helps to converge and is reduced to a closed form

Split the original problem into multiple sub-problems, and do polynomial multiplication according to the principle of multiplication

Finally, the coefficient of the nth term is the answer to n

Two closed forms

$a_n=C_m^n$ , $g\left(x\right)=\sum C_m^n{a}^n=(1+x{)}^m$ (binomial theorem)

$a_n=C_m^n$ , $g\left(x\right)=\sum C_{m+n}^n{a}^n=(1-x{)}^{m+1}$