%I #18 Mar 23 2017 10:23:22
%S 1,1,1,3,1,6,1,15,43,43,1,595,1,430,6007,25455,1,92379,1,1679601,
%T 1385671,58787,1,163809451,701149021,742901,414315331,13675080331,1,
%U 404155466746,1,1489913284351,145862174641,129644791,278607172289161,1851800127304981,1
%N Number of Young tableaux with n=i*j cells and type i*j matrices with i>=j.
%C a(p) = 1 for prime p. - _Alois P. Heinz_, Jul 25 2012
%H Alois P. Heinz, <a href="/A067231/b067231.txt">Table of n, a(n) for n = 1..350</a>
%F 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.
%F a(n) = n! * Sum_{i|n, i>=sqrt(n)} Product_{k=0..n/i-1} k!/(i+k)!. - _Alois P. Heinz_, Jul 25 2012
%p with(numtheory):
%p a:= n-> n!*add(mul(k!/(i+k)!, k=0..n/i-1),
%p i=select(d-> is(d>=sqrt(n)), divisors(n))):
%p seq(a(n), n=1..40); # _Alois P. Heinz_, Jul 25 2012
%t 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 *)
%Y Cf. A000085, A060854, A067228.
%K easy,nonn
%O 1,4
%A _Naohiro Nomoto_, Feb 20 2002