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%I #20 Mar 09 2018 06:28:22
%S 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,
%T 20,22,22,22,22,22,22,23,24,26,25,25,25,26,26,26,27,29,31,29,29,29,29,
%U 29,30,31,32,33,35,33,33,33,33,33,34,34,35,36,38,40,37,37,37,37,37,37,38,38,39,41,42,45
%N Expected rounded number of draws until two persons simultaneously drawing cards with replacement from two decks of cards with m and n cards, respectively, both obtain complete collections, written as triangle T(m,n), 1 <= n <= m.
%C This is the two-person version of the coupon collector's problem.
%H IBM Research, <a href="https://www.research.ibm.com/haifa/ponderthis/solutions/February2018.html">Ponder This Challenge February 2018</a>. Solution for 3 persons from Robert Lang.
%F 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.
%e 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.
%e The triangle starts:
%e 1
%e 3 4
%e 6 6 7
%e 8 8 9 10
%e 11 11 12 12 14
%e 15 15 15 15 16 18
%e 18 18 18 18 19 20 22
%e 22 22 22 22 22 23 24 26
%e 25 25 25 26 26 26 27 29 31
%e ...
%Y Cf. A073593, A090582, A135736 (first column in triangle), A300306 (diagonal in triangle).
%K nonn,tabl
%O 1,2
%A _Hugo Pfoertner_, Mar 07 2018
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