OFFSET
1,2
COMMENTS
From Hsin-Chieh Liao, Mar 25 2021: (Start)
Sum of coefficients of the Schur expansion of sum of Eulerian quasisymmetric functions Q_n,d over d from 0 to n-1.
a(n) is the number of marked tableaux with cells filled with 1,2,...,n. In Stembridge's paper, he gave a refinement of this number by the shape and the index of the tableaux. (End)
LINKS
Ludovic Schwob, Table of n, a(n) for n = 1..43
Ludovic Schwob, Sage program
John Shareshian and Michelle. L. Wachs, Eulerian quasisymmetric functions, Advanced in Mathematics, 225(6) (2010), 2921-2966.
John R. Stembridge, Eulerian numbers, tableaux, and the Betti numbers of a toric variety, Discrete Mathematics, 99 (1992), 307-320.
EXAMPLE
We have p(4) + p(22) + 2 p(31) + 3 p(211) + p(1111) = 8 s(4) + 2 s(22) + 4 s(31), which has sum of coefficients a(4) = 14.
PROG
(Sage) # See Links - Ludovic Schwob, Sep 26 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 14 2018
EXTENSIONS
a(11) onwards from Ludovic Schwob, Sep 26 2023
STATUS
approved