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A094219
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Number of permutations of length n with exactly 3 occurrences of the pattern 2-13.
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8
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0, 0, 0, 0, 7, 112, 1092, 8400, 56100, 341088, 1939938, 10498488, 54679625, 276276000, 1362040680, 6580248480, 31256180280, 146350008000, 676868787000, 3097351569312, 14042319855102, 63144549413792, 281895309883000
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OFFSET
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1,5
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REFERENCES
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R. Lie, Permutations and Patterns, Master's Thesis, Goeteborg, Sweden: Chalmers University of Technology, 2004.
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LINKS
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FORMULA
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a(n) = (1/3)*binomial(n+2,2)*binomial(2*n,n-5).
G.f.: (-7*x^2+8*x-2-(4*x^7+14*x^6+84*x^5-350*x^4+350*x^3-147*x^2+28*x-2) /(1-4*x)^(5/2)) /(2*x^5). - Mark van Hoeij, Apr 30 2013
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MATHEMATICA
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Table[Binomial[n + 2, 2] Binomial[2 n, n - 5]/3, {n, 1, 30}] (* Vincenzo Librandi, Aug 20 2015 *)
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PROG
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(PARI) a(n)=1/3*binomial(n+2, 2)*binomial(2*n, n-5)
(Magma) [(1/3)*Binomial(n+2, 2)*Binomial(2*n, n-5): n in [1..30]]; // Vincenzo Librandi, Aug 20 2015
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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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