%I #34 Nov 22 2018 12:18:29

%S 1,2,6,16,42,106,268,660,1618,3922,9438,22540,53528,126358

%N a(n) is the total multiplicity of all products of Schur functions s(lambda)*s(lambda) with lambda a partition of n.

%C Diagonal of the matrix formed by products of all pairs of partitions.

%C Conjecture: a(n) is the number of domino tilings of diagrams of integer partitions of 2n. - _Gus Wiseman_, Feb 25 2018

%C The above conjecture is not true, see A304662. - _Alois P. Heinz_, May 22 2018

%F a(n) = A304662(n) for n < 7. - _Alois P. Heinz_, May 22 2018

%e for n=2,

%e s(2)*s(2) = s(4) + s(3,1) + s(2,2) and

%e s(1,1) * s(1,1) = s(2,2) + s(2,1,1) + s(1,1,1,1)

%e for 6 terms in total.

%t Table[Sum[Length[LRRule[\[Lambda], \[Lambda]]], {\[Lambda], Partitions[n]}], {n, 0, 7}];

%t (* Uses the Mathematica toolbox for Symmetric Functions from A296624. *)

%Y Cf. A296624, A296626, A304662.

%K nonn,hard,more

%O 0,2

%A _Wouter Meeussen_, Dec 17 2017

%E a(13)-a(14) from _Wouter Meeussen_, Nov 22 2018