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%I #9 Mar 09 2018 17:52:05
%S 1,4,7,10,14,18,22,26,31,35,40,45,49,54,59,64,69,74,79,85,90,95,101,
%T 106,112,117,123,128,134,139,145,151,157,162,168,174,180,186,192,198,
%U 204,210,216,222,228,234,240,246,252,258,264,271,277,283,289,296,302,308,315,321,327,334
%N Expected rounded number of draws until two persons simultaneously drawing cards with replacement from two separate decks of n cards, both obtain complete collections.
%C Coupon collector's problem for two persons.
%F a(n) = round(1 - Sum_{j=0..n} Sum_{k=0..n} ( (-1)^(2*n-j-k) * binomial(n,j) * binomial(n,k) * j * k / (n^2-j*k) )) excluding term with j=k=n in summation.
%e a(1)=1, a(2)=round(11/3)=3, a(3)=round(1909/280)=7, a(4)=round(4687/455)=10, a(5)=round(7517050763/535422888)=14.
%Y Cf. A300305 (diagonal in triangle).
%K nonn
%O 1,2
%A _Hugo Pfoertner_, Mar 07 2018
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