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

1,2

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

Cf. A001951, A194102.

Sequence in context: A000828 A296676 A281910 * A111394 A140363 A280921

Adjacent sequences: A180733 A180734 A180735 * A180737 A180738 A180739

Keyword

nonn,nice

Author

Clark Kimberling, Jan 22 2011

Status

approved