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A091674
Numerator Q of probability P = Q(n)/365^(n-1) that two or more out of n people share the same birthday.
2
1, 1093, 795341, 481626601, 262130079485, 132974790903865, 64157156143943045, 29808728817823292065, 13447118719710220490765, 5923562823392985950002825, 2558600264156303883127171925, 1087010123072386037371040127025
OFFSET
2,2
COMMENTS
A 365-day year and a uniform distribution of birthdays throughout the year are assumed.
LINKS
Patrice Le Conte, Coincident Birthdays.
Mathforum at Drexel, The Birthday Problem, Ask Dr. Math: FAQ.
Eric Weisstein's World of Mathematics, Birthday Problem.
FORMULA
Q(n) = (1 - Product_{i=1..n-1} (1-i/365))*365^(n-1).
MATHEMATICA
Q[n_] := (1 - Product[(1 - i/365), {i, 1, n - 1}])365^(n - 1); Table[ Q[n], {n, 2, 13}] (* Robert G. Wilson v, Feb 05 2004 *)
CROSSREFS
Cf. A014088, A091673 (probabilities for exactly two), A091715 (probabilities for three or more).
Sequence in context: A203858 A115192 A307220 * A022197 A259909 A124122
KEYWORD
frac,nonn
AUTHOR
Hugo Pfoertner, Feb 03 2004
EXTENSIONS
More terms from Robert G. Wilson v, Feb 05 2004
STATUS
approved