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Sum of the coefficients in the Schur expansion of Product_{1<=i<=j<=n} (1+x_i+x_j), which is the total Chern class for the vector bundle Sym^2(E) where E is a vector bundle over a smooth complex projective variety of rank n with Chern roots x_1,...,x_n.
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%I #23 Sep 05 2020 20:04:40

%S 3,16,147,2304,61347,2768896,211579212,27349221376,5977081440300,

%T 2207706749337600,1377785820669766875

%N Sum of the coefficients in the Schur expansion of Product_{1<=i<=j<=n} (1+x_i+x_j), which is the total Chern class for the vector bundle Sym^2(E) where E is a vector bundle over a smooth complex projective variety of rank n with Chern roots x_1,...,x_n.

%C Also, the sum of 2^{number of 1's in T} summed over all reverse flagged fillings T of partition shape contained in (n,n-1,...,1) with row i bounded by n-i.

%H S. Billey, B. Rhoades, and V. Tewari, <a href="https://arxiv.org/abs/1902.11165">Boolean product polynomials, Schur positivity, and Chern plethysm</a>, arXiv:1902.11165 [math.CO], 2019.

%H A. Lascoux, <a href="https://gallica.bnf.fr/ark:/12148/bpt6k62341359/f397.image">Classes de Chern d'un produit tensoriel</a>, C. R. Acad. Sci. Paris Ser. A-B286 (1978), 385--387.

%Y Cf. A005130.

%K nonn,more

%O 1,1

%A _Sara Billey_, Feb 12 2019