%I A005345 M1820
%S A005345 1,2,7,160,332381,2751884514766,272622932796281408879065987,
%T A005345 3641839910835401567626683593436003894250931310990279692,
%U A005345 8488318679138307609866711262930009181182976351816002488394806142550595390781362210191324152475517251448179589\
               05
%N A005345 Number of elements of a free idempotent monoid on n letters.
%C A005345 An idempotent monoid satisfies the equation xx=x for any element x.
%C A005345 A square-free word may be equivalent to a smaller or larger word as a 
               consequence of the idempotent equation.
%D A005345 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005345 M. Lothaire, Combinatorics on Words. Addison-Wesley, Reading, MA, 1983, 
               p. 32.
%H A005345 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Monoid.html">Link to a section of The World of Mathematics.</a>
%H A005345 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               FreeIdempotentMonoid.html">Free Idempotent Monoid</a>
%H A005345 <a href="Sindx_Mo.html#monoids">Index entries for sequences related to 
               monoids</a>
%F A005345 a(n) = Sum C(n, k) Prod (k-i+1)^(2^i), i=1..k; k=0..n.
%F A005345 Binomial transform of A030450. - Michael Somos Oct 22 2006
%o A005345 (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 A005345 A030449(n)=a(n)-1.
%Y A005345 Sequence in context: A101799 A062617 A064607 this_sequence A077746 A159034 
               A120381
%Y A005345 Adjacent sequences: A005342 A005343 A005344 this_sequence A005346 A005347 
               A005348
%K A005345 nonn,easy
%O A005345 0,2
%A A005345 N. J. A. Sloane (njas(AT)research.att.com), Jeffrey Shallit
%E A005345 One more term from Gabriel Cunningham (gcasey(AT)mit.edu), Nov 14 2004