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, 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.

Links

Table of n, a(n) for n=1..62.

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

Adjacent sequences: A300303 A300304 A300305 * A300307 A300308 A300309

Keyword

nonn

Author

Hugo Pfoertner, Mar 07 2018

Status

approved