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A005345 Number of elements of a free idempotent monoid on n letters.
(Formerly M1820)
2
1, 2, 7, 160, 332381, 2751884514766, 272622932796281408879065987, 3641839910835401567626683593436003894250931310990279692, 848831867913830760986671126293000918118297635181600248839480614255059539078136221019132415247551725144817958905 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
An idempotent monoid satisfies the equation xx=x for any element x.
A squarefree word may be equivalent to a smaller or larger word as a consequence of the idempotent equation.
REFERENCES
M. Lothaire, Combinatorics on Words. Addison-Wesley, Reading, MA, 1983, p. 32.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Eric Weisstein's World of Mathematics, Monoid.
Eric Weisstein's World of Mathematics, Free Idempotent Monoid
FORMULA
a(n) = Sum_{k=0..n} (C(n, k) Prod_{i=1..k} (k-i+1)^(2^i)).
Binomial transform of A030450. - Michael Somos, Oct 22 2006
PROG
(PARI) {a(n)=sum(k=0, n, binomial(n, k)*prod(i=1, k, (k-i+1)^2^i))} /* Michael Somos, Oct 22 2006 */
CROSSREFS
A030449(n) = a(n) - 1.
Sequence in context: A207139 A064607 A182974 * A174366 A177798 A077746
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
One more term from Gabriel Cunningham (gcasey(AT)mit.edu), Nov 14 2004
STATUS
approved

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Last modified July 20 14:42 EDT 2024. Contains 374453 sequences. (Running on oeis4.)