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

Author

Enrique Navarrete, Mar 22 2017

Keywords

• nonn

Comments

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

Examples

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

Links

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

Crossrefs

Also 362880 times A176735.

Cf. A068106.

Programs

Mathematica

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

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.