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A284205 Ninth column of Euler's difference table in A068106. 0
0, 0, 0, 0, 0, 0, 0, 40320, 322560, 2943360, 30078720, 339696000, 4196666880, 56255149440, 812752093440, 12585067447680, 207863095910400, 3646938237505920, 67723519234210560, 1326863186062565760, 27349945952061841920, 591598086412112035200 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 28 06:57 EDT 2021. Contains 347703 sequences. (Running on oeis4.)