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combinat[bell] - compute Bell numbers
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Description
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The procedure bell computes the  th Bell number if the argument n is an integer; otherwise, it returns the unevaluated function call. For the BellB polynomials see BellB.
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The Bell numbers are defined by the exponential generating function:
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The Bell numbers are computed using the umbral definition :
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where bell()^n represents bell(n).
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The  th Bell number has several interesting interpretations, including
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the number of rhyming schemes in a stanza of  lines
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the number of ways n unlike objects can be placed in  like boxes
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the number of ways a product of  distinct primes may be factored
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The command with(combinat,bell) allows the use of the abbreviated form of this command.
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Examples
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![[bell]](/support/helpjp/helpview.aspx?si=7015/file03538/math122.png)
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