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Mathematica > Mathematics and Algorithms > Discrete Mathematics > Combinatorial Functions > BellB >

BellB

BellB[n]
gives the Bell number

gives the Bell polynomial

The tenth Bell number:

The fifth Bell polynomial:

The tenth Bell number:

Out[1]=

The fifth Bell polynomial:

Out[1]=

Evaluate numerically:

The precision of the output tracks the precision of the input:

BellB threads element-wise over lists:

BellB can be applied to a power series:

BellB numbers versus their asymptotics:

Compute the first 10 :

Generating function:

Sum can give results involving BellB:

Use FullSimplify to simplify expressions involving BellB:

Compute Bell numbers directly from set partitions:

Compute Bell numbers using generalized Bell polynomials:

The first argument of BellB must be a non-negative integer:

Integral representation for Bell numbers by Cesàro: