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A280425
Sixth column of Euler's difference table in A068106.
3
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
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
KEYWORD
nonn
AUTHOR
Enrique Navarrete, Jan 02 2017
STATUS
approved