A178718 Duplicate of A104779.

1, 3, 7, 21, 57, 182, 565, 1931, 6670, 24537, 92337, 364602, 1477148, 6219031, 26875932, 119930947, 548688443, 2580814003, 12425175838, 61302331782, 309055818656, 1592723862598, 8374123173858, 44917765035082, 245452258746785, 1366116578058731, 7736098938006873, 44558958700083896

Offset

1,2

Comments

a(n) is the number of symmetric nonnegative integer matrices with sum of entries equal to n, no zero rows or columns, and weakly decreasing row and column sums. - Ludovic Schwob, Aug 29 2023

Links

Ludovic Schwob, Table of n, a(n) for n = 1..39

E. Egge et al., From quasisymmetric expansions to Schur expansions via a modified inverse Kostka matrix

E. Egge et al., From quasisymmetric expansions to Schur expansions via a modified inverse Kostka matrix, European Journal of Combinatorics, Volume 31, Issue 8, December 2010, Pages 2014-2027.

Wouter Meeussen, Schur Polynomials

Wouter Meeussen, Kostka numbers up to partitions of 20

Wouter Meeussen, Mathematica code for 'kostka' function

Ludovic Schwob, On the enumeration of double cosets and self-inverse double cosets, arXiv:2506.04007 [math.CO], 2025. See p. 13.

Example

For n=4, {1,1,1,1,1} + {0,1,1,2,3} + {0,0,1,1,2} + {0,0,0,1,3} + {0,0,0,0,1} = 21.

Mathematica

(* See Meeussen link. *)

Crossrefs

Row sums of A104778.

Sequence in context: A374721 A375016 A104779 * A244897 A091650 A096240

Adjacent sequences: A178715 A178716 A178717 * A178719 A178720 A178721

Keyword

dead

Author

Wouter Meeussen, Dec 26 2010

Extensions

a(21) onwards from Ludovic Schwob, Feb 22 2023

Status

approved