A284206 Tenth column of Euler's difference table in A068106.

0, 0, 0, 0, 0, 0, 0, 0, 362880, 3265920, 33022080, 369774720, 4536362880, 60451816320, 869007242880, 13397819541120, 220448163358080, 3854801333416320, 71370457471716480, 1394586705296776320, 28676809138124407680, 618948032364173877120

Offset

1,9

Comments

For n >= 10, this is the number of permutations of [n] that avoid substrings j(j+9), 1 <= j <= n-9.

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>=10: a(n) = Sum_{j=0..n-9} (-1)^j*binomial(n-9,j)*(n-j)!.

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

Example

a(13)=4536362880 since this is the number of permutations in S13 that avoid substrings {1(10),2(11),3(12),4(13)}.

Mathematica

Table[Sum[(-1)^j*Binomial[n - 9, j]*(n - j)!, {j, 0, n - 9}], {n, 22}] (* Michael De Vlieger, Apr 03 2017 *)

Crossrefs

Also 362880 times A176735.

Cf. A068106.

Sequence in context: A011520 A321845 A226888 * A179736 A045511 A029577

Adjacent sequences: A284203 A284204 A284205 * A284207 A284208 A284209

Keyword

nonn

Author

Enrique Navarrete, Mar 22 2017

Status

approved