

A209673


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


12



1, 1, 4, 19, 116, 751, 5552, 43219, 366088, 3245311, 30569012, 299662672, 3079276708, 32773002718, 362512238272, 4136737592323, 48773665308176, 591313968267151, 7375591544495636, 94340754464144215, 1237506718985945656, 16608519982801477908, 228013066931927465872
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OFFSET

0,3


COMMENTS

Main diagonal of triangle A191714.
a(n) is also the number of semistandard Young tableaux of size and maximal entry n.  Christian Stump, Oct 09 2015


LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..500
Wikipedia, Symmetric Polynomials
FindStat  Combinatorial Statistic Finder, Semistandard Young tableaux


MATHEMATICA

(* see A191714 *)
Tr /@ Table[(stanley[#, l] & /@ Partitions[l]), {l, 11}]


CROSSREFS

Cf. A191714, A209664, A209665, A209666, A209667, A209668, A209669, A209670, A209671, A209672, A209673.
Main diagonal of A210391.  Alois P. Heinz, Mar 22 2012
Sequence in context: A013185 A186359 A203268 * A261497 A217989 A281817
Adjacent sequences: A209670 A209671 A209672 * A209674 A209675 A209676


KEYWORD

nonn


AUTHOR

Wouter Meeussen, Mar 11 2012


EXTENSIONS

a(12)a(22) from Alois P. Heinz, Mar 11 2012
Typo in Mathematica program fixed by Vaclav Kotesovec, Mar 19 2015


STATUS

approved



