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A100246
Number of permutations of {1,2,3,...,n^2} where no multiples of n are consecutive.
0
1, 12, 151200, 8219667456000, 5940854755726373683200000, 140616461430273488287535887653273600000000, 228186389638197777421971812759876473627903014249431040000000000
OFFSET
1,2
COMMENTS
limit{n->oo} a(n)/(n^2)! = 1/e.
FORMULA
a(n) = (n^2 -n)! *(n^2 -n +1)! /(n^2 -2*n +1)!.
EXAMPLE
If n = 2, we have the permutations:
1,2,3,4; 1,4,3,2; 3,2,1,4; 3,4,1,2;
2,1,3,4; 4,1,3,2; 2,3,1,4; 4,3,1,2;
2,1,4,3; 4,1,2,3; 2,3,4,1; 4,3,2,1
(no multiples of 2 are adjacent in any of the permutations). So a(2) = 12.
MAPLE
a:=n->(n^2-n)!*(n^2-n+1)!/(n^2-2*n +1)!: seq(a(n), n=1..8); # Emeric Deutsch, Aug 03 2005
CROSSREFS
Sequence in context: A328992 A069048 A284287 * A055323 A368686 A333099
KEYWORD
nonn
AUTHOR
Leroy Quet, Jan 11 2005
EXTENSIONS
More terms from Emeric Deutsch, Aug 03 2005
STATUS
approved