A284204 Eighth column of Euler's difference table in A068106.

0, 0, 0, 0, 0, 0, 5040, 35280, 287280, 2656080, 27422640, 312273360, 3884393520, 52370755920, 760381337520, 11824686110160, 196038409800240, 3450899827705680, 64272619406504880, 1262590566656060880, 26087355385405781040, 565510731026706254160

Offset: 1

Author

Enrique Navarrete, Mar 22 2017

Keywords

• nonn

Comments

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

Examples

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

Links

• Enrique Navarrete, Generalized K-Shift Forbidden Substrings in Permutations, arXiv:1610.06217 [math.CO], 2016.

Crossrefs

Also 5040 times A176733.

Cf. A068106.

Programs

Mathematica

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 *)

Formula

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

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