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I was trying to count the number of elements of order 2 in the group $S_n$ and somehow translated the problem to the following recurrence relation.

$a_{n+1} = a_n + na_{n-1}$ with the initial conditions $a_0=0, a_1=1, a_2=2$ for $n \geq 3$

I don't know how to proceed after this stage. Kindly help.

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  • $\begingroup$ Google for "linear recursion", or search on MSE - e.g., here. $\endgroup$ – Dietrich Burde Apr 19 '17 at 9:27
  • $\begingroup$ Also the number of elements of order $2$ in $S_n$ have been determined on MSE. For a start, read this question, and this one. $\endgroup$ – Dietrich Burde Apr 19 '17 at 9:28
  • $\begingroup$ the solution is not so simple, see WolframAlpha $\endgroup$ – Dr. Sonnhard Graubner Apr 19 '17 at 9:35
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    $\begingroup$ Sorry, add the condition $n \geq 3$ $\endgroup$ – joy Apr 19 '17 at 9:39
  • $\begingroup$ @ Dr. Sonnhard Graubner, kindly provide me the link. $\endgroup$ – joy Apr 19 '17 at 9:40

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