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First four terms of the sequence are doubled, then those numbers are tripled and then those numbers are quadrupled, etc.
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%I #3 Mar 30 2012 17:31:18

%S 1,2,3,4,2,4,6,8,6,12,18,24,24,48,72,96,120,240,360,480,720,1440,2160,

%T 2880,5040,10080,15120,20160,40320,80640,120960,161280,362880,725760,

%U 1088640,1451520,3628800,7257600,10886400,14515200,39916800,79833600

%N First four terms of the sequence are doubled, then those numbers are tripled and then those numbers are quadrupled, etc.

%F a(4n-3) = A000142(n). a(4n-2)=2*A000142(n)=A052849(n), a(4n-1)=3*A000142(n)=A052560(n), a(4n)=4*A000142(n)=2*A052849(n)=A052578(n).

%t Table[n!{1, 2, 3, 4}, {n, 11}] // Flatten

%Y Cf. A000142, A115425.

%K nonn

%O 1,2

%A _Robert G. Wilson v_, Apr 25 2006