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

1,7

Comments

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

Links

Table of n, a(n) for n=1..22.

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

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.

Example

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

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 *)

Crossrefs

Also 5040 times A176733.

Cf. A068106.

Sequence in context: A147632 A321843 A226886 * A159083 A179731 A061140

Adjacent sequences: A284201 A284202 A284203 * A284205 A284206 A284207

Keyword

nonn

Author

Enrique Navarrete, Mar 22 2017

Status

approved