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.

A284206 Tenth column of Euler's difference table in A068106.

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%I A284206 #8 Apr 06 2017 21:26:40
%S A284206 0,0,0,0,0,0,0,0,362880,3265920,33022080,369774720,4536362880,
%T A284206 60451816320,869007242880,13397819541120,220448163358080,
%U A284206 3854801333416320,71370457471716480,1394586705296776320,28676809138124407680,618948032364173877120
%N A284206 Tenth column of Euler's difference table in A068106.
%C A284206 For n >= 10, this is the number of permutations of [n] that avoid substrings j(j+9), 1 <= j <= n-9.
%H A284206 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 A284206 For n>=10: a(n) = Sum_{j=0..n-9} (-1)^j*binomial(n-9,j)*(n-j)!.
%F A284206 Note a(n)/n! ~ 1/e.
%e A284206 a(13)=4536362880 since this is the number of permutations in S13 that avoid substrings {1(10),2(11),3(12),4(13)}.
%t A284206 Table[Sum[(-1)^j*Binomial[n - 9, j]*(n - j)!, {j, 0, n - 9}], {n, 22}] (* _Michael De Vlieger_, Apr 03 2017 *)
%Y A284206 Also 362880 times A176735.
%Y A284206 Cf. A068106.
%K A284206 nonn
%O A284206 1,9
%A A284206 _Enrique Navarrete_, Mar 22 2017