OFFSET
1,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..425
Vaclav Kotesovec, Graph - The asymptotic ratio (10^8 terms)
FORMULA
a(n) = [r]*[2r]*...[nr], where r=sqrt(2) and []=floor.
a(n) ~ c * 2^(n/2) * n! / n^(1/(2*sqrt(2))), where c = 0.71779404... - Vaclav Kotesovec, Oct 02 2018
EXAMPLE
a(n) = 1*2*4*5*7*...*floor(n*sqrt(2)).
MAPLE
r:=sqrt(2): seq(mul(floor(k*r), k=1..n), n=1..25); # Muniru A Asiru, Sep 29 2018
MATHEMATICA
Table[Product[Floor[i*Sqrt[2]], {i, n}], {n, 1, 25}] (* modified by G. C. Greubel, Sep 29 2018 *)
PROG
(PARI) for(n=1, 25, print1(prod(j=1, n, floor(j*sqrt(2))), ", ")) \\ G. C. Greubel, Sep 29 2018
(Magma) [(&*[Floor(j*Sqrt(2)): j in [1..n]]): n in [1..25]]; // G. C. Greubel, Sep 29 2018
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
Clark Kimberling, Jan 22 2011
STATUS
approved