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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
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
FindStat - Combinatorial Statistic Finder, Semistandard Young tableaux
MATHEMATICA
(* see A191714 *)
Tr /@ Table[(stanley[#, l] & /@ Partitions[l]), {l, 11}]
CROSSREFS
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