A284207 Eleventh column of Euler's difference table in A068106.

0, 0, 0, 0, 0, 0, 0, 0, 0, 3628800, 36288000, 402796800, 4906137600, 64988179200, 929459059200, 14266826784000, 233845982899200, 4075249496774400, 75225258805132800, 1465957162768492800, 30071395843421184000, 647624841502298284800

Offset: 1

Author

Enrique Navarrete, Mar 22 2017

Keywords

• nonn

Comments

For n >= 11, this is the number of permutations of [n] that avoid substrings j(j+10), 1 <= j <= n-10.

Examples

			a(14)=64988179200 since this is the number of permutations in S14 that avoid substrings {1(11),2(12),3(13),4(14)}.
		

Links

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

Crossrefs

Also 3628800 times A176736.

Cf. A068106.

Programs

Mathematica

Table[Sum[(-1)^j*Binomial[n - 10, j]*(n - j)!, {j, 0, n - 10}], {n, 22}] (* Michael De Vlieger, Apr 03 2017 *)

Formula

For n>=11: a(n) = Sum_{j=0..n-10} (-1)^j*binomial(n-10,j)*(n-j)!.

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