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

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

Offset: 0

Author

Vladimir Reshetnikov, Nov 25 2015

Keywords

• nonn
• cons

Examples

			0.7731926563792859874827625676...
		

References

• 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.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..188
• Eric Weisstein's World of Mathematics, Dobiński's Formula, Poisson Distribution.
• Wikipedia, Dobinski's formula, Poisson distribution.

Crossrefs

Cf. A000110, A229837.

Programs

Mathematica

RealDigits[SequenceLimit[1`100 Accumulate[Table[k^(1/2)/(E k!), {k, 100}]]], 10, 85][[1]] (* or *)
RealDigits[NExpectation[x^(1/2), Distributed[x, PoissonDistribution[1]], WorkingPrecision -> 110], 10, 100][[1]]