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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

Table of n, a(n) for n=0..8.

Eric Weisstein's World of Mathematics, Monoid.

Eric Weisstein's World of Mathematics, Free Idempotent Monoid

Index entries for sequences related to monoids

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

Adjacent sequences:  A005342 A005343 A005344 * A005346 A005347 A005348

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Jeffrey Shallit

EXTENSIONS

One more term from Gabriel Cunningham (gcasey(AT)mit.edu), Nov 14 2004

STATUS

approved

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Last modified November 20 12:37 EST 2018. Contains 317402 sequences. (Running on oeis4.)