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%I A003127 M3537 #17 Feb 03 2015 09:00:56
%S A003127 0,1,4,17,70,282,1136,4583,18457,74131,296945,1190344,4773949,
%T A003127 19145523,76751393,307503585,1231182078,4929075135,19736248104,
%U A003127 79031964989,316476142454,1267191674419,5073155081395,20306187559891,81265371486027
%N A003127 Value of an urn with n balls of type -1 and n balls of type +1.
%D A003127 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A003127 W. M. Boyce, <a href="http://dx.doi.org/10.1016/0012-365X(73)90123-4">On a simple optimal stopping problem</a>, Discr. Math., 5 (1973), 297-312.
%F A003127 a(n) = B(n, n) where B(n, m) is defined in A003125. - _Sean A. Irvine_, Feb 02 2015
%t A003127 w[a_, 0] = a; w[0, b_] = 0; w[a_, b_] := w[a, b] = Max[ (a(1 + w[a-1, b]) + b(-1 + w[a, b-1])) / (a+b), 0]; Table[w[n, n] * Binomial[2n, n], {n, 0, 40}] (* _Joel B. Lewis_, Aug 27 2009 *)
%K A003127 nonn
%O A003127 1,3
%A A003127 _N. J. A. Sloane_
%E A003127 More terms from _Joel B. Lewis_, Aug 27 2009
%E A003127 Title clarified by _Sean A. Irvine_, Feb 02 2015

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