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A284206
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Tenth column of Euler's difference table in A068106.
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1
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0, 0, 0, 0, 0, 0, 0, 0, 362880, 3265920, 33022080, 369774720, 4536362880, 60451816320, 869007242880, 13397819541120, 220448163358080, 3854801333416320, 71370457471716480, 1394586705296776320, 28676809138124407680, 618948032364173877120
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OFFSET
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1,9
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COMMENTS
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For n >= 10, this is the number of permutations of [n] that avoid substrings j(j+9), 1 <= j <= n-9.
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LINKS
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FORMULA
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For n>=10: a(n) = Sum_{j=0..n-9} (-1)^j*binomial(n-9,j)*(n-j)!.
Note a(n)/n! ~ 1/e.
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EXAMPLE
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a(13)=4536362880 since this is the number of permutations in S13 that avoid substrings {1(10),2(11),3(12),4(13)}.
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MATHEMATICA
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Table[Sum[(-1)^j*Binomial[n - 9, j]*(n - j)!, {j, 0, n - 9}], {n, 22}] (* Michael De Vlieger, Apr 03 2017 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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