What's my telephone number? Introduction

The telephone numbers or involution numbers are a sequence of integers that count the ways \$n\$ telephone lines can be connected to each other, where each line can be connected to at most one other line. These were first studied by Heinrich August Rothe in 1800, when he gave a recurrence equation where they may be calculated. It is sequence A000085 in the OEIS.

Some help


The first terms of the sequence are \$1, 1, 2, 4, 10, 26, 76, 232, 764, 2620, 9496\$
It can be described by the recurrence relation \$T(n)=T(n-1)+(n-1)T(n-2)\$ (starting from \$n=0\$)
It can be expressed exactly by the summation \$T(n)=\sum\limits_{k=0}^{\lfloor n/2 \rfloor}{n\choose 2k}(2k-1)!!=\sum\limits_{k=0}^{\lfloor n/2 \rfloor}\frac{n!}{2^k(n-2k)!k!}\$ (starting from \$n=0\$)
There are other ways to get the telephone numbers which can be found on the Wikipedia and OEIS pages 


Challenge

Write a program or function which returns the \$n^{th}\$ telephone number.

I/O examples

(0 based indexing)
input --&gt; output

0  --&gt;            1
10 --&gt;         9496
16 --&gt;     46206736
22 --&gt; 618884638912


Rules


Input will be the index of the sequence
The index origin can be anything
As the numbers can get very large, you only need to support numbers as large as your language can handle
Standard I/O rules apply
No standard loopholes
This is code-golf so shortest code in bytes wins
Python, 33 bytes



f=lambda n:n&lt;2or~-n*f(n-2)+f(n-1)


Try it online!

Uses the recursive formula.