

A105350


Largest squared factorial dividing n!.


2



1, 1, 1, 4, 4, 36, 36, 576, 576, 518400, 518400, 518400, 518400, 25401600, 25401600, 1625702400, 1625702400, 131681894400, 131681894400, 13168189440000, 13168189440000, 1593350922240000, 1593350922240000, 229442532802560000
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OFFSET

1,4


COMMENTS

a(n) = A001044(A056039(n)) = A056038(n)^2.
From Emeric Deutsch, Dec 24 2008: (Start)
a(n) is the number of permutations of {1,2,...,n} with no even entry followed by a smaller entry. Example: a(4)=4 because we have 1234, 1324, 3124 and 2314.
a(n) is the number of permutations p of {1,2,...,n} such that p(j) is odd whenever j is even. Example: a(4)=4 because we have 4123, 2143, 2341 and 4321.
a(n) = A134434(n,0). (End)


LINKS

Table of n, a(n) for n=1..24.
S. Kitaev and J. Remmel, Classifying descents according to parity, arXiv:math/0508570 [math.CO], 2005; Annals of Combinatorics, 11, 2007, 173193. [Emeric Deutsch, Dec 24 2008]
Index entries for sequences related to factorial numbers.


FORMULA

a(2n1) = a(2n) = (n!)^2.  Emeric Deutsch, Dec 24 2008


MAPLE

seq(factorial(ceil((1/2)*n))^2, n = 1 .. 24); # Emeric Deutsch, Dec 24 2008


MATHEMATICA

a[n_] := (For[k = 1, Divisible[n!, k!^2], k++]; (k1)!^2)
Table[a[n], {n, 1, 24}] (* JeanFrançois Alcover, Aug 07 2018 *)


CROSSREFS

Cf. A000142, A000290, A055771.
Cf. A134434.  Emeric Deutsch, Dec 24 2008
Sequence in context: A227511 A249807 A180064 * A126936 A129357 A100303
Adjacent sequences: A105347 A105348 A105349 * A105351 A105352 A105353


KEYWORD

nonn


AUTHOR

Reinhard Zumkeller, Apr 01 2005


EXTENSIONS

Data and offset corrected by JeanFrançois Alcover, Aug 07 2018


STATUS

approved



