I would appreciate if somebody could help me with the following problem:
Q: How to find $a_n=?$
$$(n+1)a_{n+2}-na_{n+1}-a_{n}=0,a_1=1, a_2=0$$
I would appreciate if somebody could help me with the following problem:
Q: How to find $a_n=?$
$$(n+1)a_{n+2}-na_{n+1}-a_{n}=0,a_1=1, a_2=0$$
This question appears to be off-topic. The users who voted to close gave this specific reason:
Hint: Let us multiply both sides by $n!$
$(n+1)!a_{n+2}=n(n!a_{n+1})+n((n-1)!a_{n})$
We now let $(n-1)!a_n=b_n$
$b_{n+2}=n(b_{n+1}+b_n)$
Now, it is a recurrence form similar to derangement.