A180736 a(n) = [r]*[2r]*...[nr], where r=sqrt(2) and []=floor.

1, 2, 8, 40, 280, 2240, 20160, 221760, 2661120, 37255680, 558835200, 8941363200, 160944537600, 3057946214400, 64216870502400, 1412771151052800, 33906507625267200, 847662690631680000, 22039229956423680000, 617098438779863040000, 17895854724616028160000, 554771496463096872960000

Offset: 1

Author

Clark Kimberling, Jan 22 2011

Keywords

• nonn
• nice

Examples

			a(n) = 1*2*4*5*7*...*floor(n*sqrt(2)).
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..425
• Vaclav Kotesovec, Graph - The asymptotic ratio (10^8 terms)

Crossrefs

Cf. A001951, A194102.

Programs

Magma

[(&*[Floor(j*Sqrt(2)): j in [1..n]]): n in [1..25]]; // G. C. Greubel, Sep 29 2018

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 *)

PARI

for(n=1,25, print1(prod(j=1,n, floor(j*sqrt(2))), ", ")) \\ G. C. Greubel, Sep 29 2018

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