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%I #9 Jun 25 2022 21:57:02
%S 1,1,2,3,4,6,10,20,36,72,162,352,810,1872,4480,11088,27720,71280,
%T 186368,496128,1347192,3720960,10407936,29576988,85322160,249500160,
%U 738904320,2216712960,6732000000,20680540160,64257392640,201852518400,640832000000,2055425699250,6658777165824,21781337550336
%N Factorial splitting: write n! = x*y*z with x <= y <= z and minimal z-x; sequence gives value of z.
%C Apparently we have x < y < z for all n > 9. If so, using strict inequalities x < y < z in the definition would make the sequence undefined for n < 3 and affect only a(9) by switching from 9! = 70*72*72 to 9! = 63*72*80.
%H Max Alekseyev, <a href="/A355191/b355191.txt">Table of n, a(n) for n = 0..100</a>
%Y Cf. A061030, A061031, A061032, A061033, A060776, A060777, A060795, A060796, A200743, A200744, A355189, A355190, A355192.
%K nonn
%O 0,3
%A _Max Alekseyev_, Jun 23 2022