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%I #11 May 21 2015 17:56:42
%S 1,2,6,6,30,20,140,70,630,7,77,924,12012,3432,51480,12870,218790,
%T 48620,923780,184756,3879876,705432,16224936,2704156,67603900,
%U 10400600,280816200,178296,5170584,155117520,4808643120,601080390,19835652870
%N a(n) = n!/(k!)^2, where k is the largest number such that (k!)^2 divides n!.
%C Least integer of the form n!/{(n-k)!}^2.
%C Similar to but different from A001405.
%H Ivan Neretin, <a href="/A056042/b056042.txt">Table of n, a(n) for n = 1..1000</a>
%e E.g. for n=9, 10, 11, 12, a(n)=630, 7, 77, 924 while the corresponding central binomial coefficients are 126, 252, 462, 924 respectively.
%t f[n_] := Min[ Select[ Table[ n!/(n - k)!^2, {k, n}], IntegerQ[ # ] &]]; Table[ f[n], {n, 33}] (_Robert G. Wilson v_)
%Y Cf. A000142, A001405, A000188, A055772, A096123, A096125.
%K nonn
%O 1,2
%A _Labos Elemer_, Jul 25 2000
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