OFFSET
1,2
COMMENTS
This is the two-person version of the coupon collector's problem.
LINKS
IBM Research, Ponder This Challenge February 2018. Solution for 3 persons from Robert Lang.
FORMULA
T(m,n) = round(1 - Sum_{j=0..m} Sum_{k=0..n} ( (-1)^(m-j+n-k) * binomial(m,j) * binomial(n,k) * j * k / (m*n-j*k) )) excluding term with j=m and k=n in summation.
EXAMPLE
T(1,1)=1, T(2,1)=3, T(2,2)=round(11/3)=4, T(3,1)=round(11/2)=6, T(3,2)=round(57/10)=6, T(3,3)=round(1909/280)=7.
The triangle starts:
1
3 4
6 6 7
8 8 9 10
11 11 12 12 14
15 15 15 15 16 18
18 18 18 18 19 20 22
22 22 22 22 22 23 24 26
25 25 25 26 26 26 27 29 31
...
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Hugo Pfoertner, Mar 07 2018
STATUS
approved