A067700

[Joseph S. Myers]

In sequence A067700, the formula given as the name of the sequence, the
numbers given for the sequence and the description given in the comments
yield three different sequences.

The name is "a(n) = 2*(n^2)!/n!*Product_{k = 0 .. n-1 } k!/(n+k)!.".  This
yields:

2,2,14,2002,11685817,4643452871486,188521303279519793344,
1095306299241168174546015616610,1214623999201248600771350941956671886496775

The sequence given however is:
2,4,84,48048,1402298040,3343286067469920,950147368528779758457120,
44162749985403900797695349661715200,
440762756830149092247907829817237094171949712000

(which looks like it matches the formula if "/n!" is removed).

The comments say "Number of distinct-integer n^2-arrangements(or
n^2-tuples) free of any monotonic increasing or decreasing
(n+1)-subsequence.".  This sequence, however, starts 1,4,1764,577152576.
This looks like it may match the formula if the "2*" and "/n!" are both
removed, then the result is squared (yielding "a(n) =
((n^2)!*Product_{k = 0 .. n-1 } k!/(n+k)!)^2."), though I don't have a
proof of this.

-- 
Joseph S. Myers
jsm28 at cam.ac.uk