A056042 a(n) = n!/(k!)^2, where k is the largest number such that (k!)^2 divides n!.

1, 2, 6, 6, 30, 20, 140, 70, 630, 7, 77, 924, 12012, 3432, 51480, 12870, 218790, 48620, 923780, 184756, 3879876, 705432, 16224936, 2704156, 67603900, 10400600, 280816200, 178296, 5170584, 155117520, 4808643120, 601080390, 19835652870

Offset: 1

Author

Labos Elemer, Jul 25 2000

Keywords

• nonn

Comments

Least integer of the form n!/{(n-k)!}^2.

Similar to but different from A001405.

Examples

			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.
		

Links

• Ivan Neretin, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000142, A001405, A000188, A055772, A096123, A096125.

Programs

Mathematica

f[n_] := Min[ Select[ Table[ n!/(n - k)!^2, {k, n}], IntegerQ[ # ] &]]; Table[ f[n], {n, 33}] (Robert G. Wilson v)