cp's OEIS Frontend

A225177 Numerator of answer to sock-sorting problem with n socks.

%I A225177 #41 Dec 22 2016 22:06:33
%S A225177 1,5,35,311,3377,43373,643475,10831151,203961377,4248732053,
%T A225177 97006864835,2409006894311,64645920431057,1864195055263613,
%U A225177 57489983163699635,1888035573701458271,65785247971229129537,2423878578219411790373,94161366504933859099235,3846438440798147117812631
%N A225177 Numerator of answer to sock-sorting problem with n socks.
%C A225177 Here is the problem as presented in Technology Review.
%C A225177 "... Fred Tydeman owns N pairs of socks, each pair a different color, which he washes when all of them are dirty. When the washing and drying are complete, he uses the following algorithm for sorting and storing the socks. Tydeman first brings the entire basket of clean socks up to the bedroom, removes one sock, and lays it on the bed. He then removes another sock at random. If the new sock matches any on the bed (initially there is only one there), he folds the pair and places it in a drawer. If there is no match, the new sock is placed on the bed and another sock is taken from the basket, again at random. Tydeman repeats the procedure until all the socks are matched and records the maximum number of unmatched socks on the bed. He would like to know the expected value of this maximum in terms of N...."
%C A225177 It appears that the expectation can be written as a(n)/b(n), where b(n) = A001147(n) is the product of the first n odd numbers. (This is certainly true for n <= 10.) The sequence gives the values of a(n).
%D A225177 Allan Gottlieb, editor, Problem M/J-2, MIT Technology Review, May-June 2013.
%H A225177 Paul Tek, <a href="/A225177/b225177.txt">Table of n, a(n) for n = 1..300</a>
%H A225177 Milton Eisner, <a href="http://www.jstor.org/stable/3027327">Problem 216</a>, The Two-Year College Mathematics Journal, Vol. 13, No. 3, Jun., 1982, page 206.
%H A225177 Wenbo V. Li, Geoffrey Pritchard, <a href="http://dx.doi.org/10.1007/978-3-0348-8829-5_14">A central limit theorem for the sock-sorting problem</a>, In "High Dimensional Probability" (Oberwolfach, 1996), 245-248, Progr. Probab., 43, Birkhäuser, Basel, 1998.
%H A225177 David Steinsaltz, <a href="http://dx.doi.org/10.1214/EJP.v4-51">Random time changes for sock-sorting and other stochastic process limit theorems</a>, Electron. J. Probab. 4 (1999), no. 14, 25 pp.
%H A225177 Paul Tek, <a href="/A225177/a225177.txt">PARI program for this sequence</a>
%e A225177 The expectations in lowest terms are 1, 5/3, 7/3, 311/105, 3377/945, 3943/945, 18385/3861, 10831151/2027025, 203961377/34459425, 4248732053/654729075, ...
%Y A225177 Cf. A001147.
%K A225177 nonn,frac
%O A225177 1,2
%A A225177 _N. J. A. Sloane_, May 01 2013, based on an email from _Jerrold Grossman_, Apr 27 2013