YACCP: Coupon collector: Pull 20 coupons per time

Question

Yet-another-coupon-collector's-problem:
I know this may be a very similar question to others, but I couldn't crack it and this one has a 'special knack' to it, please bear with me:

1. 260 specific coupons are in the pool (will give you completely random coupons every time, not taking into account what it gave out already)
2. you pull 20 (random, but all different) coupons out per try (this is the 'special knack')
3. how many times do you have to pull until you pulled 100% of the coupons
4. (follow-up: how many times do you have to pull until you pulled ~95% )

(Complete flabbergastedness:

• How to input this problem in wolframalpha?
• How to calculate this using the browser console (vanilla javascript))

thanks, any help a lot appreciated

Answer 1

I found this Formula for approximating this problem, I hope you guys agree:

$$\frac{log(1−x/260)}{log(1−20/260)}$$

(where t batches of size b drawn from n different coupons)

That would yield the following results: for 247 (95%) different coupons: 37.45 times