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3 questions
4
votes
1
answer
287
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A 2nd order recursion with polynomial coefficients
I'm hoping to find "exact" an solution to the following simple recursion:
$q_m(j+1) = m \cdot q_m(j) + j(j+m)\cdot q_m(j-1)$
with initial data $q_m(0) = 1$, $q_m(1)=m$, where $m \geq 0$ is an ...
6
votes
3
answers
372
views
Second order recurrence relation for third order polynomial root
Consider this recurrence relation:
$$
\begin{eqnarray*}
f_0&=&1\\
f_n&=&
\sum_{m=0}^{n-1} \frac{\left(\frac{m+3}{2}\right)_{m-1}}{\left(\frac{m+2}{2}\right)_m} f_{n-m-1} f_m\ \ \ \...
- 237
4
votes
1
answer
231
views
Product of polynomial coefficients of a recurrence
A recurrence is given by
$f[0]=2x$, $f[1]=3x^3-x^2+x+1$,
$$
f[n]=(x^{2^n}+1)f[n-1]+(x^{2^n}+1)(x^{2^n-1}+1)
$$
How does the PRODUCT of the nonzero coefficients of $f[n]$ scale with $n$?
