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A280920
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Seventh column of Euler's difference table in A068106.
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2
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0, 0, 0, 0, 0, 720, 4320, 30960, 256320, 2399760, 25022880, 287250480, 3597143040, 48773612880, 711607724640, 11113078385520, 184925331414720, 3265974496290960, 61006644910213920, 1201583921745846960, 24885771463659934080, 540624959563046320080, 12291921453805577987040
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OFFSET
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1,6
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COMMENTS
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For n >= 7, this is the number of permutations of [n] that avoid substrings j(j+6), 1 <= j <= n-6.
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LINKS
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FORMULA
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For n>=7: a(n) = Sum_{j=0..n-6} (-1)^j*binomial(n-6,j)*(n-j)!.
Note a(n)/n! ~ 1/e.
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EXAMPLE
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a(10)=2399760 since there are 2399760 permutations in S10 that avoid substrings {17,28,39,4(10)}.
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MATHEMATICA
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Table[Sum[(-1)^j*Binomial[n-6, j]*(n-j)!, {j, 0, n-6}], {n, 1, 23}] (* Indranil Ghosh, Feb 26 2017 *)
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PROG
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(Python)
f=math.factorial
def C(n, r):return f(n)/f(r)/f(n-r)
....s=0
....for j in range(0, n-5):
........s+=(-1)**j*C(n-6, j)*f(n-j)
(PARI) a(n) = sum(j=0, n-6, (-1)^j*binomial(n-6, j)*(n-j)!); \\ Michel Marcus, Feb 26 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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