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%I #22 Jul 02 2015 07:58:06
%S 1,2,2,4,2,12,2,30,44,86,2,1190,2,860,12014,26886,2,184758,2,3359202,
%T 2771342,117574,2,327618902,701149022,1485802,828630662,27350160662,2,
%U 808310933492,2,2979826568702,291724349282,259289582,557214344578322,2031957220875002,2
%N Number of rectangular standard Young tableaux with n cells.
%C Number of ways to arrange the numbers 1, 2, .., n=i*j into an i*j rectangle so that each row and each column is increasing.
%C a(p) = 2 for prime p. - _Alois P. Heinz_, Jul 25 2012
%H Alois P. Heinz, <a href="/A067228/b067228.txt">Table of n, a(n) for n = 1..350</a>
%F a(n) = n! * Sum_{i|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), i=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, Divisors[n]}]; Table[a[n], {n, 1, 40}] (* _Jean-François Alcover_, Jul 02 2015, after _Alois P. Heinz_ *)
%Y Cf. A000085, A060854, A067231.
%Y Column k=0 of A238707.
%K easy,nonn
%O 1,2
%A _Naohiro Nomoto_, Feb 20 2002
%E Better name from _Joerg Arndt_, Feb 24 2014
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