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
Keywords
Examples
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).
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.
Comments