A one variable data table is quite ideal for this ..
You have the formula in B1: =SUM(A1:A20)
(B1 is the output cell of interest)
Put in C10: =B1
(just a simple link to the output cell)
Fill* the numbers 1,2,3, ... into B11:B10000,
i.e. into a range just to the left of the output range in C11:C10000
*Put in B11: 1, in B12: 2, then select B11:B12 and fill down to B10000
Select B10:C10000
Click Data > Table
Leave the "Row input cell" box empty
Put in Column input cell: B10 (say*)
Click OK
*Can be any empty cell in the vicinity of the selected range, e.g.: B9
In C11:C10000 will be computed 9,990 randomized results for B1
Each press of F9 will generate afresh another 9,990 sets
Freeze the results elsewhere via a copy > paste special > values
Adapt to suit ..
Note that although the TABLE function (e.g.: {=TABLE(,B10)} ) will appear in
every cell in C11:C10000 and looks very much like an array formula, it
cannot just be entered as such. The construct of the data table must be
done / invoked via the Data > Table menu / steps outlined
And as data tables are calc-intensive, you might also want to switch the
calc mode from "Automatic" to either "Automatic except tables" or "Manual"
(via checking the option in: Tools > Options > Calculation tab)