OFFSET
1,4
COMMENTS
a(p) = 1 for prime p. - Alois P. Heinz, Jul 25 2012
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..350
FORMULA
a(n) = number of ways to arrange the numbers 1, 2, .., n=i*j in i*j matrices so that each row and each column is increasing. Here i and j satisfy i >= j.
a(n) = n! * Sum_{i|n, i>=sqrt(n)} Product_{k=0..n/i-1} k!/(i+k)!. - Alois P. Heinz, Jul 25 2012
MAPLE
with(numtheory):
a:= n-> n!*add(mul(k!/(i+k)!, k=0..n/i-1),
i=select(d-> is(d>=sqrt(n)), divisors(n))):
seq(a(n), n=1..40); # Alois P. Heinz, Jul 25 2012
MATHEMATICA
a[n_] := n!*Sum[Product[k!/(i+k)!, {k, 0, n/i-1}], {i, Select[Divisors[n], # >= Sqrt[n]&]}]; Table[a[n], {n, 1, 40}] (* Jean-François Alcover, Mar 23 2017, translated from Maple *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Naohiro Nomoto, Feb 20 2002
STATUS
approved