Vector of non-negative integers.
Values greater than 218 return an Inf.
Non-integers or negative values return a NaN.
Author
T. W. Yee
Details
The Bell numbers emerge from a series expansion of
\( \exp(e^x - 1)\)
for real \(x\).
The first few values are
\(B_{0}=1\),
\(B_{1}=1\),
\(B_{2}=2\),
\(B_{3}=5\),
\(B_{4}=15\).
The series increases quickly so that overflow occurs when
its argument is more than 218.
References
Bell, E. T. (1934).
Exponential polynomials.
Ann. Math.,
35, 258--277.
Bell, E. T. (1934).
Exponential numbers.
Amer. Math. Monthly,
41, 411--419.