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A056174
Number of non-monotone maps from 1,...,n to 1,...,n.
1
0, 0, 0, 10, 190, 2878, 45738, 820118, 16764354, 387371878, 9999815254, 285310965190, 8916097744112, 302875096191666, 11112006785441430, 437893890225741870, 18446744073108471242, 827240261884003157974, 39346408075287462440142, 1978419655660278243860198
OFFSET
0,4
FORMULA
a(n) = n^n - C(2n, n) + n = A000312(n) - A045992(n)
EXAMPLE
a(3)=10 since the mappings of (1,2,3) to (1,2,1), (1,3,1), (1,3,2), (2,1,2), (2,1,3), (2,3,1), (2,3,2), (3,1,2), (3,1,3) and (3,2,3) all reverse direction
CROSSREFS
KEYWORD
nonn
AUTHOR
Henry Bottomley, Jul 27 2000
EXTENSIONS
More terms from Sean A. Irvine, Apr 15 2022
STATUS
approved