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A300306
Expected rounded number of draws until two persons simultaneously drawing cards with replacement from two separate decks of n cards, both obtain complete collections.
1
1, 4, 7, 10, 14, 18, 22, 26, 31, 35, 40, 45, 49, 54, 59, 64, 69, 74, 79, 85, 90, 95, 101, 106, 112, 117, 123, 128, 134, 139, 145, 151, 157, 162, 168, 174, 180, 186, 192, 198, 204, 210, 216, 222, 228, 234, 240, 246, 252, 258, 264, 271, 277, 283, 289, 296, 302, 308, 315, 321, 327, 334
OFFSET
1,2
COMMENTS
Coupon collector's problem for two persons.
FORMULA
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.
EXAMPLE
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.
CROSSREFS
Cf. A300305 (diagonal in triangle).
Sequence in context: A161187 A273287 A310692 * A310693 A310694 A310695
KEYWORD
nonn
AUTHOR
Hugo Pfoertner, Mar 07 2018
STATUS
approved