

A296624


a(n) is the total multiplicity of all products of Schur functions s(lambda)*s(mu) with partition lambda >= mu and size(lambda) + size(mu)= n.


3



1, 1, 4, 7, 20, 37, 90, 171, 378, 721, 1500, 2843, 5682, 10661, 20674
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OFFSET

0,3


COMMENTS

The condition lambda >= mu restricts the results to the lower triangular part of the matrix formed by products of all pairs of partitions.
'Multiplicity' signifies that terms like k*s(nu) count as k terms.


LINKS



EXAMPLE

For n=3 we have
s(3)*s(0) = s(3); s(2,1)*s(0) = s(2,1); s(1,1,1)*s(0) = s(1,1,1)
s(2)*s(1) = s(3) + s(2,1) and
s(1,1)*s(1) = s(2,1) + s(1,1,1)
for a total of 3+2+2 = 7 terms.


MATHEMATICA

Tr/@ Table[Sum[
Length[LRRule[\[Lambda], \[Mu]]], {\[Lambda],
Partitions[n  i]}, {\[Mu],
If[2 i === n, Join[{\[Lambda]}, lesspartitions[\[Lambda]]],
Partitions[i]]}], {n, 14}, {i, 0, Floor[(n)/2]}]; (* Uses functions defined in the 'Toolbox for symmetric functions', see Links. *)


CROSSREFS



KEYWORD

nonn,hard,more


AUTHOR



STATUS

approved



