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

1,5

Comments

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

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.

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.

Example

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

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 *)

Crossrefs

Also 120 times A001910.

Cf. A068106.

Sequence in context: A234437 A090216 A265041 * A235768 A179963 A229568

Adjacent sequences: A280422 A280423 A280424 * A280426 A280427 A280428

Keyword

nonn

Author

Enrique Navarrete, Jan 02 2017

Status

approved