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%I #45 Sep 22 2023 05:35:32
%S 1,3,7,21,57,182,565,1931,6670,24537,92337,364602,1477148,6219031,
%T 26875932,119930947,548688443,2580814003,12425175838,61302331782,
%U 309055818656,1592723862598,8374123173858,44917765035082,245452258746785,1366116578058731,7736098938006873,44558958700083896
%N a(n) is the sum of entries of n-th Kostka matrix for the partitions of n.
%C 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
%H Ludovic Schwob, <a href="/A178718/b178718.txt">Table of n, a(n) for n = 1..39</a>
%H E. Egge et al., <a href="https://web.archive.org/web/20120103121601/http://www.cems.uvm.edu/~gwarring/research/kinv9.pdf">From quasisymmetric expansions to Schur expansions via a modified inverse Kostka matrix</a>
%H E. Egge et al., <a href="https://doi.org/10.1016/j.ejc.2010.05.010">From quasisymmetric expansions to Schur expansions via a modified inverse Kostka matrix</a>, European Journal of Combinatorics, Volume 31, Issue 8, December 2010, Pages 2014-2027.
%H Wouter Meeussen, <a href="http://users.telenet.be/Wouter.Meeussen/ToolBox.nb">Schur Polynomials</a>
%H Wouter Meeussen, <a href="/A178718/a178718.txt">Kostka numbers up to partitions of 20</a>
%H Wouter Meeussen, <a href="/A178718/a178718_1.txt">Mathematica code for 'kostka' function</a>
%e 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.
%t See Meeussen link.
%Y Row sums of A104778.
%K nonn
%O 1,2
%A _Wouter Meeussen_, Dec 26 2010
%E a(21) onwards from _Ludovic Schwob_, Feb 22 2023
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