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A213090
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Number of permutations of length n whose associated Schubert variety is defined by inclusions.
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1
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1, 1, 2, 6, 23, 101, 477, 2343, 11762, 59786, 306132, 1574536, 8120782, 41957030, 217021682, 1123371986, 5817788471, 30139492189, 156174965473, 809382185187, 4195096032623, 21745137658765, 112720985668763, 584336632836945, 3029232133574325, 15703985220888071
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OFFSET
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0,3
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COMMENTS
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Permutations avoiding the four permutation patterns 4231, 35142, 42513, 351624.
See references for several other characterizations.
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LINKS
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Vic Reiner, Richard Stanley, and Joel Lewis, P0011 in the Database of Permutation Pattern Avoidance.
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FORMULA
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G.f.: 1 + (1-3*x-2*x^2-(1-x-2*x^2)*sqrt(1-4*x)) / (1-3*x-(1-x+2*x^2) * sqrt(1-4*x)). - Michael Albert, Jan 15 2013
D-finite with recurrence n*a(n) +(-15*n+16)*a(n-1) +(77*n-158)*a(n-2) +(-149*n+408)*a(n-3) +2*(39*n-55)*a(n-4) +4*(-8*n+7)*a(n-5) +16*(-2*n+11)*a(n-6)=0. - R. J. Mathar, May 30 2014
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MATHEMATICA
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1 + ((1 - 5x - 2x^2 + 8x^3) - Sqrt[1-4x] (1 - 5x - 2x^2))/(2(1 - 6x + 5x^2 - 4x^3)) + O[x]^26 // CoefficientList[#, x]& (* Jean-François Alcover, Nov 28 2018 *)
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PROG
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(PARI) (1-3*x-2*x^2-(1-x-2*x^2)*sqrt(1-4*x))/(1-3*x-(1-x+2*x^2)*sqrt(1-4*x)) \\ Charles R Greathouse IV, Oct 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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