A306397 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.

3, 16, 147, 2304, 61347, 2768896, 211579212, 27349221376, 5977081440300, 2207706749337600, 1377785820669766875

Offset

1,1

Comments

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.

Links

Table of n, a(n) for n=1..11.

S. Billey, B. Rhoades, and V. Tewari, Boolean product polynomials, Schur positivity, and Chern plethysm, arXiv:1902.11165 [math.CO], 2019.

A. Lascoux, Classes de Chern d'un produit tensoriel, C. R. Acad. Sci. Paris Ser. A-B286 (1978), 385--387.

Crossrefs

Cf. A005130.

Sequence in context: A006058 A121588 A331538 * A264660 A362655 A368451

Adjacent sequences: A306394 A306395 A306396 * A306398 A306399 A306400

Keyword

nonn,more

Author

Sara Billey, Feb 12 2019

Status

approved