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A280425 Sixth column of Euler's difference table in A068106. 1

%I

%S 0,0,0,0,120,600,3720,27240,229080,2170680,22852200,264398280,

%T 3332744760,45440868120,666166856520,10446911529000,174478419885720,

%U 3091496076405240,57915148833808680,1143668772912038280,23742102690747895800,516882856872298424280,11775038596933279562760

%N Sixth column of Euler's difference table in A068106.

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

%H Indranil Ghosh, <a href="/A280425/b280425.txt">Table of n, a(n) for n = 1..400</a>

%H Enrique Navarrete, <a href="http://arxiv.org/abs/1610.06217">Generalized K-Shift Forbidden Substrings in Permutations</a>, arXiv:1610.06217 [math.CO], 2016.

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

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

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

%t 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 *)

%Y Also 120 times A001910.

%Y Cf. A068106.

%K nonn

%O 1,5

%A _Enrique Navarrete_, Jan 02 2017

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Last modified September 27 00:14 EDT 2020. Contains 337378 sequences. (Running on oeis4.)