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A264806 Decimal expansion of the Bell number with index 1/2 calculated using Dobiński's formula. 1

%I

%S 7,7,3,1,9,2,6,5,6,3,7,9,2,8,5,9,8,7,4,8,2,7,6,2,5,6,7,6,0,5,9,0,3,0,

%T 0,7,8,9,4,9,3,3,1,0,6,6,2,7,6,2,0,6,8,6,9,5,9,5,3,5,8,2,5,8,3,6,3,0,

%U 0,1,7,2,8,7,0,2,8,3,9,4,7,7,9,4,4

%N Decimal expansion of the Bell number with index 1/2 calculated using Dobiński's formula.

%D G. Dobiński, Summierung der Reihe Sum(n^m/n!) für m = 1, 2, 3, 4, 5, . . ., Grunert Archiv (Arch. f. Math. und Physik), 61 (1877) 333-336.

%H G. C. Greubel, <a href="/A264806/b264806.txt">Table of n, a(n) for n = 0..188</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Dobinski%27s_formula">Dobinski's formula</a>, <a href="http://en.wikipedia.org/wiki/Poisson_distribution#Higher_moments">Poisson distribution</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DobinskisFormula.html">Dobiński's Formula</a>, <a href="http://mathworld.wolfram.com/PoissonDistribution.html#eqn22">Poisson Distribution</a>.

%e 0.7731926563792859874827625676...

%t RealDigits[SequenceLimit[1`100 Accumulate[Table[k^(1/2)/(E k!), {k, 100}]]], 10, 85][[1]] (* or *)

%t RealDigits[NExpectation[x^(1/2), Distributed[x, PoissonDistribution[1]], WorkingPrecision -> 110], 10, 100][[1]]

%Y Cf. A000110.

%K nonn,cons

%O 0,1

%A _Vladimir Reshetnikov_, Nov 25 2015

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Last modified April 5 10:33 EDT 2020. Contains 333239 sequences. (Running on oeis4.)