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%I M1820 #23 May 20 2014 22:35:45
%S 1,2,7,160,332381,2751884514766,272622932796281408879065987,
%T 3641839910835401567626683593436003894250931310990279692,
%U 848831867913830760986671126293000918118297635181600248839480614255059539078136221019132415247551725144817958905
%N Number of elements of a free idempotent monoid on n letters.
%C An idempotent monoid satisfies the equation xx=x for any element x.
%C A squarefree word may be equivalent to a smaller or larger word as a consequence of the idempotent equation.
%D M. Lothaire, Combinatorics on Words. Addison-Wesley, Reading, MA, 1983, p. 32.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Monoid.html">Monoid.</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/FreeIdempotentMonoid.html">Free Idempotent Monoid</a>
%H <a href="/index/Mo#monoids">Index entries for sequences related to monoids</a>
%F a(n) = Sum_{k=0..n} (C(n, k) Prod_{i=1..k} (k-i+1)^(2^i)).
%F Binomial transform of A030450. - _Michael Somos_, Oct 22 2006
%o (PARI) {a(n)=sum(k=0, n, binomial(n, k)*prod(i=1, k, (k-i+1)^2^i))} /* _Michael Somos_, Oct 22 2006 */
%Y A030449(n) = a(n) - 1.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, _Jeffrey Shallit_
%E One more term from Gabriel Cunningham (gcasey(AT)mit.edu), Nov 14 2004
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