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%I #21 Feb 16 2022 23:39:54
%S 1,2,8,40,280,2240,20160,221760,2661120,37255680,558835200,8941363200,
%T 160944537600,3057946214400,64216870502400,1412771151052800,
%U 33906507625267200,847662690631680000,22039229956423680000,617098438779863040000,17895854724616028160000,554771496463096872960000
%N a(n) = [r]*[2r]*...[nr], where r=sqrt(2) and []=floor.
%H G. C. Greubel, <a href="/A180736/b180736.txt">Table of n, a(n) for n = 1..425</a>
%H Vaclav Kotesovec, <a href="/A180736/a180736.jpg">Graph - The asymptotic ratio (10^8 terms)</a>
%F a(n) = [r]*[2r]*...[nr], where r=sqrt(2) and []=floor.
%F a(n) ~ c * 2^(n/2) * n! / n^(1/(2*sqrt(2))), where c = 0.71779404... - _Vaclav Kotesovec_, Oct 02 2018
%e a(n) = 1*2*4*5*7*...*floor(n*sqrt(2)).
%p r:=sqrt(2): seq(mul(floor(k*r),k=1..n),n=1..25); # _Muniru A Asiru_, Sep 29 2018
%t Table[Product[Floor[i*Sqrt[2]], {i, n}], {n, 1, 25}] (* modified by _G. C. Greubel_, Sep 29 2018 *)
%o (PARI) for(n=1,25, print1(prod(j=1,n, floor(j*sqrt(2))), ", ")) \\ _G. C. Greubel_, Sep 29 2018
%o (Magma) [(&*[Floor(j*Sqrt(2)): j in [1..n]]): n in [1..25]]; // _G. C. Greubel_, Sep 29 2018
%Y Cf. A001951, A194102.
%K nonn,nice
%O 1,2
%A _Clark Kimberling_, Jan 22 2011
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