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A280425 Sixth column of Euler's difference table in A068106. 1
0, 0, 0, 0, 120, 600, 3720, 27240, 229080, 2170680, 22852200, 264398280, 3332744760, 45440868120, 666166856520, 10446911529000, 174478419885720, 3091496076405240, 57915148833808680, 1143668772912038280, 23742102690747895800, 516882856872298424280, 11775038596933279562760 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 9 23:26 EDT 2020. Contains 336335 sequences. (Running on oeis4.)