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A005345
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Number of elements of a free idempotent monoid on n letters.
(Formerly M1820)
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2
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1, 2, 7, 160, 332381, 2751884514766, 272622932796281408879065987, 3641839910835401567626683593436003894250931310990279692, 848831867913830760986671126293000918118297635181600248839480614255059539078136221019132415247551725144817958905
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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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.
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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).
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LINKS
| Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Eric Weisstein's World of Mathematics, Free Idempotent Monoid
Index entries for sequences related to monoids
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FORMULA
| a(n) = Sum C(n, k) Prod (k-i+1)^(2^i), i=1..k; k=0..n.
Binomial transform of A030450. - Michael Somos Oct 22 2006
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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 */
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CROSSREFS
| A030449(n)=a(n)-1.
Sequence in context: A062617 A064607 A182974 * A174366 A177798 A077746
Adjacent sequences: A005342 A005343 A005344 * A005346 A005347 A005348
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jeffrey Shallit
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EXTENSIONS
| One more term from Gabriel Cunningham (gcasey(AT)mit.edu), Nov 14 2004
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