A317553 Sum of coefficients in the expansion of Sum_{y a composition of n} p(y) in terms of Schur functions, where p is power-sum symmetric functions.

1, 2, 5, 14, 39, 122, 387, 1328, 4675, 17414, 66743, 267234, 1100453, 4696414, 20580433, 92966560, 430394961, 2046068386, 9950230149, 49544789182, 251930150903, 1308655057210, 6931418152099, 37435337021328, 205874622937315, 1152718809407558, 6564213262312871

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

Cf. A000085, A082733, A153452, A296188, A296561, A300121, A304438, A317552, A317554.

Sequence in context: A151409 A339289 A003054 * A148316 A148317 A148318

Adjacent sequences: A317550 A317551 A317552 * A317554 A317555 A317556

Keyword

nonn

Author

Gus Wiseman, Sep 14 2018

Extensions

a(11) onwards from Ludovic Schwob, Sep 26 2023

Status

approved