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%I #15 Sep 03 2018 22:59:54
%S 2,7,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,
%T 3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,
%U 3,1,3,1,3,1,3
%N Decimal expansion of constant arising in clubbed binomial approximation for the lightbulb process.
%C In the so-called lightbulb process, on days r = 1, ..., n, out of n lightbulbs, all initially off, exactly r bulbs selected uniformly and independent of the past have their status changed from off to on, or vice versa. With W_n the number of bulbs on at the terminal time n and C_n a suitable clubbed binomial distribution, d_{TV}(W_n,C_n) <= 2.7314 sqrt{n} e^{-(n+1)/3} for all n >= 1.
%C This is the value of the function g_1(9) after eq (16) of the preprint.
%H Larry Goldstein, Aihua Xia, <a href="http://arxiv.org/abs/1111.3984">Clubbed Binomial Approximation for the Lightbulb Process</a>, arXiv:1111.3984v1 [math.PR], Nov 16, 2011.
%e 2.731313... = 1352/495.
%o (PARI) 1352/495. \\ _Charles R Greathouse IV_, Nov 29 2011
%K nonn,cons
%O 1,1
%A _Jonathan Vos Post_, Nov 17 2011
%E Corrected by _R. J. Mathar_, Nov 29 2011
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