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.

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

Alois P. Heinz, Table of n, a(n) for n = 0..500

FindStat - Combinatorial Statistic Finder, Semistandard Young tableaux

Wikipedia, Symmetric Polynomials

Mathematica

(* see A191714 *)
Tr /@ Table[(stanley[#, l] & /@ Partitions[l]), {l, 11}]
(* or *)
Table[SeriesCoefficient[1/((1-x)^(n*(n+1)/2) * (1+x)^(n*(n-1)/2)), {x, 0, n}], {n, 0, 25}] (* Vaclav Kotesovec, Aug 06 2025 *)

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: A353607 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