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Idempotent Number

The idempotent numbers are given by

B_(n,k)(1,2,3,...)=(n; k)k^(n-k),

where B_(n,k) is a Bell polynomial and (n; k) is a binomial coefficient. A table of the first few is given below.

n=1n=2n=3n=4n=5n=6n=7
kA000027A001788A036216A040075A050982A050988A050989
11
221
3361
4424121
558090201
66240540240301
7767228352240525421
88179213608179207000100856
9946086123612902478750181441764
10101152026244086016078750027216041160

See also

Bell Polynomial, Lah Number

Explore with Wolfram|Alpha

References

Comtet, L. Advanced Combinatorics: The Art of Finite and Infinite Expansions, rev. enl. ed. Dordrecht, Netherlands: Reidel, p. 91, 1974.Roman, S. The Umbral Calculus. New York: Academic Press, p. 85, 1984.Sloane, N. J. A. Sequences A000027/M0472, A001788/M4161, A036216, A040075, A050982, A050988, and A050989 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Idempotent Number

Cite this as:

Weisstein, Eric W. "Idempotent Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/IdempotentNumber.html

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