A030450 Related to number of elements in the free band (idempotent semigroup) on n generators.
1, 1, 4, 144, 331776, 2751882854400, 272622932796264897576960000, 3641839910835401567626683591527643364677019238400000000
Offset: 0
Keywords
References
- John M. Howie, Fundamentals of Semigroup Theory, Oxford University Press 1995, p. 123.
Programs
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Mathematica
s=1;lst={};Do[AppendTo[lst,s*=s*=n],{n,9}];lst (* Vladimir Joseph Stephan Orlovsky, Oct 20 2009 *) Fold[Append[#1, (#2 Last[#1])^2] &, {1}, Range@ 7] (* Michael De Vlieger, Dec 03 2017 *) -
PARI
{a(n) = if(n<0, 0, prod(i=1, n, (n-i+1)^2^i))}; /* Michael Somos, Oct 22 2006 */ -
Sage
def A030450(n) : return prod((n-i+1)^(2^i) for i in (1..n)) [A030450(n) for n in (0..9)] # Jani Melik, Jun 06 2015
Formula
Binomial transform is A005345. - Michael Somos, Oct 22 2006
a(n) = (n*a(n-1))^2 if n > 0. a(0)=1. - Michael Somos, Oct 22 2006
a(n) = Product_{i=1..n} (n-i+1)^(2^i).
Sum_{n>=1} 1/a(n) = A258621. - Amiram Eldar, Nov 19 2020
Comments