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A284207
Eleventh column of Euler's difference table in A068106.
1
0, 0, 0, 0, 0, 0, 0, 0, 0, 3628800, 36288000, 402796800, 4906137600, 64988179200, 929459059200, 14266826784000, 233845982899200, 4075249496774400, 75225258805132800, 1465957162768492800, 30071395843421184000, 647624841502298284800
OFFSET
1,10
COMMENTS
For n >= 11, this is the number of permutations of [n] that avoid substrings j(j+10), 1 <= j <= n-10.
LINKS
Enrique Navarrete, Generalized K-Shift Forbidden Substrings in Permutations, arXiv:1610.06217 [math.CO], 2016.
FORMULA
For n>=11: a(n) = Sum_{j=0..n-10} (-1)^j*binomial(n-10,j)*(n-j)!.
Note a(n)/n! ~ 1/e.
EXAMPLE
a(14)=64988179200 since this is the number of permutations in S14 that avoid substrings {1(11),2(12),3(13),4(14)}.
MATHEMATICA
Table[Sum[(-1)^j*Binomial[n - 10, j]*(n - j)!, {j, 0, n - 10}], {n, 22}] (* Michael De Vlieger, Apr 03 2017 *)
CROSSREFS
Also 3628800 times A176736.
Cf. A068106.
Sequence in context: A011521 A321846 A226889 * A061603 A153761 A133132
KEYWORD
nonn
AUTHOR
Enrique Navarrete, Mar 22 2017
STATUS
approved