%I #46 Nov 17 2018 15:33:42

%S 1,1,4,19,116,751,5552,43219,366088,3245311,30569012,299662672,

%T 3079276708,32773002718,362512238272,4136737592323,48773665308176,

%U 591313968267151,7375591544495636,94340754464144215,1237506718985945656,16608519982801477908,228013066931927465872

%N a(n) = count of monomials, of degree k=n, in the Schur symmetric polynomials s(mu,k) summed over all partitions mu of n.

%C Main diagonal of triangle A191714.

%C a(n) is also the number of semistandard Young tableaux of size and maximal entry n. - _Christian Stump_, Oct 09 2015

%H Alois P. Heinz, <a href="/A209673/b209673.txt">Table of n, a(n) for n = 0..500</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Symmetric_polynomials">Symmetric Polynomials</a>

%H FindStat - Combinatorial Statistic Finder, <a href="http://www.findstat.org/SemistandardTableaux">Semistandard Young tableaux</a>

%t (* see A191714 *)

%t Tr /@ Table[(stanley[#, l] & /@ Partitions[l]), {l, 11}]

%Y Cf. A191714, A209664, A209665, A209666, A209667, A209668, A209669, A209670, A209671, A209672, A209673.

%Y Main diagonal of A210391. - _Alois P. Heinz_, Mar 22 2012

%K nonn

%O 0,3

%A _Wouter Meeussen_, Mar 11 2012

%E a(12)-a(22) from _Alois P. Heinz_, Mar 11 2012

%E Typo in Mathematica program fixed by _Vaclav Kotesovec_, Mar 19 2015