%I #9 Apr 06 2017 21:26:32

%S 0,0,0,0,0,0,5040,35280,287280,2656080,27422640,312273360,3884393520,

%T 52370755920,760381337520,11824686110160,196038409800240,

%U 3450899827705680,64272619406504880,1262590566656060880,26087355385405781040,565510731026706254160

%N Eighth column of Euler's difference table in A068106.

%C For n >= 8, this is the number of permutations of [n] that avoid substrings j(j+7), 1 <= j <= n-7.

%H Enrique Navarrete, <a href="http://arxiv.org/abs/1610.06217">Generalized K-Shift Forbidden Substrings in Permutations</a>, arXiv:1610.06217 [math.CO], 2016.

%F For n>=8: a(n) = Sum_{j=0..n-7} (-1)^j*binomial(n-7,j)*(n-j)!.

%F Note a(n)/n! ~ 1/e.

%e a(11)=27422640 since this is the number of permutations in S11 that avoid substrings {18,29,3(10),4(11)}.

%t With[{k = 8}, ConstantArray[0, k - 2]~Join~Table[Sum[(-1)^j*Binomial[n - (k - 1), j] (n - j)!, {j, 0, n - (k - 1)}], {n, k - 1, k + 12}]] (* _Michael De Vlieger_, Mar 26 2017 *)

%Y Also 5040 times A176733.

%Y Cf. A068106.

%K nonn

%O 1,7

%A _Enrique Navarrete_, Mar 22 2017