cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A284207 Eleventh column of Euler's difference table in A068106.

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%I A284207 #8 Apr 06 2017 21:26:49
%S A284207 0,0,0,0,0,0,0,0,0,3628800,36288000,402796800,4906137600,64988179200,
%T A284207 929459059200,14266826784000,233845982899200,4075249496774400,
%U A284207 75225258805132800,1465957162768492800,30071395843421184000,647624841502298284800
%N A284207 Eleventh column of Euler's difference table in A068106.
%C A284207 For n >= 11, this is the number of permutations of [n] that avoid substrings j(j+10), 1 <= j <= n-10.
%H A284207 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 A284207 For n>=11: a(n) = Sum_{j=0..n-10} (-1)^j*binomial(n-10,j)*(n-j)!.
%F A284207 Note a(n)/n! ~ 1/e.
%e A284207 a(14)=64988179200 since this is the number of permutations in S14 that avoid substrings {1(11),2(12),3(13),4(14)}.
%t A284207 Table[Sum[(-1)^j*Binomial[n - 10, j]*(n - j)!, {j, 0, n - 10}], {n, 22}] (* _Michael De Vlieger_, Apr 03 2017 *)
%Y A284207 Also 3628800 times A176736.
%Y A284207 Cf. A068106.
%K A284207 nonn
%O A284207 1,10
%A A284207 _Enrique Navarrete_, Mar 22 2017