OFFSET
1,9
COMMENTS
For n >= 10, this is the number of permutations of [n] that avoid substrings j(j+9), 1 <= j <= n-9.
LINKS
Enrique Navarrete, Generalized K-Shift Forbidden Substrings in Permutations, arXiv:1610.06217 [math.CO], 2016.
FORMULA
For n>=10: a(n) = Sum_{j=0..n-9} (-1)^j*binomial(n-9,j)*(n-j)!.
Note a(n)/n! ~ 1/e.
EXAMPLE
a(13)=4536362880 since this is the number of permutations in S13 that avoid substrings {1(10),2(11),3(12),4(13)}.
MATHEMATICA
Table[Sum[(-1)^j*Binomial[n - 9, j]*(n - j)!, {j, 0, n - 9}], {n, 22}] (* Michael De Vlieger, Apr 03 2017 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Enrique Navarrete, Mar 22 2017
STATUS
approved