New posts in Recurrence Relations

Combinatorial argument for solution of recursion behaving similarly as Pascals triangle?

Does $(n+1)(n-2)x_{n+1}=n(n^2-n-1)x_n-(n-1)^3x_{n-1}$ with $x_2=x_3=1$ define a sequence that is integral at prime indices?

Find $\lim\limits_{n\to\infty}\frac{a_1+a_2+...+a_n}{1+\frac{1}{\sqrt2}+...+\frac{1}{\sqrt{n}}}$ with $a_1=1$ and $a_{n+1}=\frac{1+a_n}{\sqrt{n+1}}$

Closed form for these polynomials?

Find all possible values of $a, p$ for which $x_{n+1} = x_n^2 + (1-2p)x_n + p^2$ converges, given $x_1 = a$ and $n\in\Bbb N$

Am I properly simplifying this geometric progression?

A more natural solution to finding the general terms of a recurrence relation in $2$ variables

How to solve this recurrence relation using generating functions: $a_n = 10 a_{n-1}-25 a_{n-2} + 5^n\binom{n+2}2$?

Freaky Polynomial: $P_n(x)=\left(x\frac{d}{dx}\right)^n f(x)$

Alphabet with 6 vowels and 12 consonants, find the amount of words without two consonants in a row.