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

Author

Wouter Meeussen, Dec 26 2010

Keywords

• dead

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

Examples

			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.
		

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.

Crossrefs

Row sums of A104778.

Programs

Mathematica

(* See Meeussen link. *)

Extensions

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