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

1,2

Comments

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

Similar to but different from A001405.

Links

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

Example

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.

Mathematica

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

Crossrefs

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

Sequence in context: A216850 A070889 A072744 * A056040 A333073 A099566

Adjacent sequences: A056039 A056040 A056041 * A056043 A056044 A056045

Keyword

nonn

Author

Labos Elemer, Jul 25 2000

Status

approved