Given that $A(x) = \frac{8 +14x-50x^2}{(1-7x^2+6x^3)}$
compute $[x^n]A(x)$
Using a generating function $A(x) = \sum_{i=0} a_kx^k $ I get $a_n - 7a_{n-2} + 6a_{n-3} = 0, n>= 3$
How do I now compute $[x^n]A(x)$?
2026-04-01 20:23:47.1775075027
how to compute $[x^n]A(x)$
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Throwing it at Wolfy, $1-7x^2+6x^3 =(-1 + x) (-1 + 2 x) (1 + 3 x) $.
Since all the roots are simple, you can now do a partial fraction decomposition $\dfrac1{1-7x^2+6x^3} =\dfrac{a}{-1+x}+\dfrac{b}{-1+2x}+\dfrac{c}{1+3x} $ to get the power series for $ \dfrac{8 +14x-50x^2}{(1-7x^2+6x^3)} $.