%I A030450
%S A030450 1,1,4,144,331776,2751882854400,272622932796264897576960000,
%T A030450 3641839910835401567626683591527643364677019238400000000
%N A030450 Related to number of elements in the free band (idempotent semigroup) 
               on n generators.
%D A030450 J. Howie, Fundamentals of Semigroup Theory, Oxford University Press 1995, 
               p. 123.
%H A030450 <a href="Sindx_Se.html#semigroups">Index entries for sequences related 
               to semigroups</a>
%F A030450 Binomial transform is A005345. - Michael Somos Oct 22 2006
%F A030450 a(n)=(n*a(n-1))^2 if n>0. a(0)=1. - Michael Somos Oct 22 2006
%F A030450 a(n) = Product_{i=1..n} (n-i+1)^(2^i).
%t A030450 s=1;lst={};Do[AppendTo[lst,s*=s*=n],{n,9}];lst [From Vladimir Orlovsky 
               (4vladimir(AT)gmail.com), Oct 20 2009]
%o A030450 (PARI) {a(n)=if(n<0, 0, prod(i=1, n, (n-i+1)^2^i))} /* Michael Somos 
               Oct 22 2006 */
%Y A030450 Cf. A030449.
%Y A030450 A052129(n)=n*a(n-1) if n>0.
%Y A030450 Sequence in context: A069135 A138176 A055209 this_sequence A041629 A159197 
               A160470
%Y A030450 Adjacent sequences: A030447 A030448 A030449 this_sequence A030451 A030452 
               A030453
%K A030450 nonn
%O A030450 0,3
%A A030450 marcel_j(AT)hilbert.maths.utas.edu.au (Marcel Jackson)