Count, Replace, Add Up! Definition

Define the nth term of the CRAU sequence as follows.


Begin with the singleton array A = [n].
Do the following n times:

For each integer k in A, replace the entry k with k natural numbers, counting from 1 to k.
Compute the sum of all integers in A.


For example, if n = 3, we start with the list [3].

We replace 3 with 1, 2, 3, yielding [1, 2, 3].

We now replace 1, 2, and 3 with 1, 1, 2 and 1, 2, 3 (resp.), yielding [1, 1, 2, 1, 2, 3].

Finally, we perform the same replacements as in the previous step for all six integers in the array, yielding [1, 1, 1, 2, 1, 1, 2, 1, 2, 3].

The sum of the resulting integers is 15, so this is the third CRAU number.

Task

Write a program of a function that, given a strictly positive integer n as input, computes the nth term of the CRAU sequence.

This is code-golf. May the shortest code in bytes win!

Test cases

 1 -&gt;       1
 2 -&gt;       4
 3 -&gt;      15
 4 -&gt;      56
 5 -&gt;     210
 6 -&gt;     792
 7 -&gt;    3003
 8 -&gt;   11440
 9 -&gt;   43758
10 -&gt;  167960
11 -&gt;  646646
12 -&gt; 2496144
13 -&gt; 9657700


Related


Simplicial polytopic numbers
OEIS A001791: Binomial coefficients C(2n,n-1)
MATL, 5 bytes
EGqXn

Try it online, or verify all test cases!
Explanation:
E       #Double the input
 Gq     #Push &quot;input - 1&quot;
   Xn   #Calculate &quot;nchoosek&quot; on the two numbers