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%I #41 Apr 06 2021 20:18:12
%S 1,2,7,28,114,472,1988,8480,36474,157720,684404,2976994,12971206,
%T 56587676,247097170,1079749976,4720841314,20649303934,90353041092,
%U 395459463960,1731251197242,7580521689750,33197447406682,145400339328566,636901149067534,2790082285204966
%N Number of smooth Schubert varieties of type C_n.
%C 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))
%H S. C. Billey, <a href="https://doi.org/10.1006/aima.1998.1744">Pattern Avoidance and Rational Smoothness of Schubert varieties</a>, Advances in Math, vol. 139 (1998) pp. 141-156.
%H E. Richmond and W. Slofstra, <a href="https://arxiv.org/abs/1510.06060">Staircase diagrams and enumeration of smooth Schubert varieties</a>, arXiv:1510.06060 [math.CO], 2015; J. Combin. Ser. A, Vol 150 (2017) pp. 328-376.
%F 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
%o (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
%Y Cf. A061539.
%K nonn,easy
%O 0,2
%A _Sara Billey_, Apr 02 2013
%E a(0)=1 prepended and a(11) and beyond added by _Edward Richmond_, Apr 05 2021