|
|
A030450
|
|
Related to number of elements in the free band (idempotent semigroup) on n generators.
|
|
6
|
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
Continued square root 2 = sqrt(1 + sqrt(1 + sqrt(4 + sqrt(144 + ...)))) = sqrt(1 + sqrt(1 + 2*sqrt(1 + 3*sqrt(1 + 4*sqrt(1 + ...)))) [S. Ramanujan]. - Michael Somos, Dec 03 2017
|
|
REFERENCES
|
John M. Howie, Fundamentals of Semigroup Theory, Oxford University Press 1995, p. 123.
|
|
LINKS
|
|
|
FORMULA
|
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).
|
|
MATHEMATICA
|
|
|
PROG
|
(PARI) {a(n) = if(n<0, 0, prod(i=1, n, (n-i+1)^2^i))}; /* Michael Somos, Oct 22 2006 */
(Sage)
return prod((n-i+1)^(2^i) for i in (1..n))
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Marcel Jackson (marcel_j(AT)hilbert.maths.utas.edu.au)
|
|
STATUS
|
approved
|
|
|
|