A284205 Ninth column of Euler's difference table in A068106.

0, 0, 0, 0, 0, 0, 0, 40320, 322560, 2943360, 30078720, 339696000, 4196666880, 56255149440, 812752093440, 12585067447680, 207863095910400, 3646938237505920, 67723519234210560, 1326863186062565760, 27349945952061841920, 591598086412112035200

Offset

1,8

Comments

For n >= 9, this is the number of permutations of [n] that avoid substrings j(j+8), 1 <= j <= n-8.

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>=9: a(n) = Sum_{j=0..n-8} (-1)^j*binomial(n-8,j)*(n-j)!.

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

Example

a(12)=339696000 since this is the number of permutations in S12 that avoid substrings {19,2(10),3(11),4(12)}.

Mathematica

With[{k = 9}, 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 40320 times A176734.

Cf. A068106.

Sequence in context: A250055 A321844 A226887 * A239035 A179734 A061123

Adjacent sequences: A284202 A284203 A284204 * A284206 A284207 A284208

Keyword

nonn

Author

Enrique Navarrete, Mar 22 2017

Status

approved