A280425 Sixth column of Euler's difference table in A068106.

0, 0, 0, 0, 120, 600, 3720, 27240, 229080, 2170680, 22852200, 264398280, 3332744760, 45440868120, 666166856520, 10446911529000, 174478419885720, 3091496076405240, 57915148833808680, 1143668772912038280, 23742102690747895800, 516882856872298424280, 11775038596933279562760

Offset: 1

Author

Enrique Navarrete, Jan 02 2017

Keywords

• nonn

Comments

For n >= 6, this is the number of permutations of [n] that avoid substrings j(j+5), 1 <= j <= n-5.

Examples

			a(9) = 229080 since there are 229080 permutations in S9 that avoid substrings {16,27,38,49}.
		

Links

• Indranil Ghosh, Table of n, a(n) for n = 1..400
• Enrique Navarrete, Generalized K-Shift Forbidden Substrings in Permutations, arXiv:1610.06217 [math.CO], 2016.

Crossrefs

Also 120 times A001910.

Cf. A068106.

Programs

Mathematica

a[1]=a[2]=a[3]=a[4]=0; a[5]=120;a[6]=600;a[n_]:=Sum[(-1)^j*Binomial[n-5,j]*(n-j)!,{j,0,n-5}];Table[a[n],{n,1,23}] (* Indranil Ghosh, Feb 25 2017 *)

Formula

For n>=6: a(n) = Sum_{j=0..n-5} (-1)^j*binomial(n-5,j)*(n-j)!.

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