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

1,10

Comments

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

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

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

Example

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

Mathematica

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

Crossrefs

Also 3628800 times A176736.

Cf. A068106.

Sequence in context: A011521 A321846 A226889 * A061603 A153761 A133132

Adjacent sequences: A284204 A284205 A284206 * A284208 A284209 A284210

Keyword

nonn

Author

Enrique Navarrete, Mar 22 2017

Status

approved