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A116765
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Number of permutations of length n which avoid the patterns 1234, 2431, 4312.
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0
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1, 2, 6, 21, 70, 195, 458, 942, 1752, 3016, 4886, 7539, 11178, 16033, 22362, 30452, 40620, 53214, 68614, 87233, 109518, 135951, 167050, 203370, 245504, 294084, 349782, 413311, 485426, 566925
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OFFSET
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1,2
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LINKS
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FORMULA
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G.f.: A(x) = -{(3x^6+6x^5-9x^4+5x^3-9x^2+4x-1)x}/{(x-1)^6}
For n >= 2, a(n) = (n^5 + 75n^4 - 715n^3 + 2685n^2 - 4446n + 2880)/120. - Franklin T. Adams-Watters, Sep 16 2006
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MAPLE
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cn := [1, -5, 11, -11, 10, 3, -5, -3] ;
p := add(cn[i]*x^(i-1), i=1..nops(cn)) ;
q := (1-x)^6 ;
taylor(p/q, x=0, 40) ;
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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