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A224066
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Number of smooth Schubert varieties of type C_n.
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0
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1, 2, 7, 28, 114, 472, 1988, 8480, 36474, 157720, 684404, 2976994, 12971206, 56587676, 247097170, 1079749976, 4720841314, 20649303934, 90353041092, 395459463960, 1731251197242, 7580521689750, 33197447406682, 145400339328566, 636901149067534, 2790082285204966
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OFFSET
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0,2
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COMMENTS
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Characterized as the signed permutations avoiding the list of patterns: '((1 -2) (-2 -1 -3) (3 -2 1) (3 -2 -1) (-3 2 -1) (-3 -2 1) (-3 -2 -1)(-2 -4 3 1) (3 4 1 2) (3 4 -1 2) (-3 4 1 2) (-3 4 -1 2)(-3 -4 -1 -2) (4 -1 3 -2) (4 2 3 1) (4 2 3 -1) (-4 2 3 1))
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LINKS
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FORMULA
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G.f.: ((1-7*x+15*x^2-11*x^3-2*x^4+5*x^5)+(x-x^2-x^3+3*x^4-x^5)*sqrt(1-4*x))/((1-x)^2*(1-6*x+8*x^2-4*x^3)). - Edward Richmond, Apr 06 2021
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PROG
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(PARI) seq(n)={Vec(((1-7*x+15*x^2-11*x^3-2*x^4+5*x^5)+(x-x^2-x^3+3*x^4-x^5)*sqrt(1-4*x + O(x^n)))/((1-x)^2*(1-6*x+8*x^2-4*x^3)))} \\ Andrew Howroyd, Apr 06 2021
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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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EXTENSIONS
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a(0)=1 prepended and a(11) and beyond added by Edward Richmond, Apr 05 2021
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STATUS
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approved
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