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Mathematica > Mathematics and Algorithms > Discrete Mathematics > Combinatorial Functions > StirlingS1 >

BUILT-IN MATHEMATICA SYMBOL

StirlingS1

gives the Stirling number of the first kind

Integer mathematical function, suitable for both symbolic and numerical manipulation.

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StirlingS1 threads element-wise over lists:

Plot Stirling numbers of the first kind on a logarithmic scale:

Plot the average number of cycles in symmetric group elements:

Generate values from the generating function:

Stirling numbers of the first kind are effectively inverses of Stirling numbers of the second kind:

Calculate large Stirling numbers of the first kind using Cauchy's theorem:

StirlingS1 can have large values for moderately sized arguments:

The value at

is defined to be 1:

Plot sums of digits: