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