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%I #10 Jun 25 2022 21:56:44
%S 1,1,1,1,2,4,8,14,32,70,140,324,768,1800,4368,10800,27300,70560,
%T 184800,494208,1343680,3704400,10388250,29560960,85250880,249318000,
%U 738720000,2216160000,6729074352,20675655000,64245312000,201819656500,640760440320
%N Factorial splitting: write n! = x*y*z with x <= y <= z and minimal z-x; sequence gives value of x.
%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="/A355189/b355189.txt">Table of n, a(n) for n = 0..100</a>
%Y Cf. A061030, A061031, A061032, A061033, A060776, A060777, A060795, A060796, A200743, A200744, A355190, A355191, A355192.
%K nonn
%O 0,5
%A _Max Alekseyev_, Jun 23 2022