OFFSET
1,1
LINKS
T. Amdeberhan, Theorems, problems and conjectures, arXiv:1207.4045 [math.RT], 2012-2015.
EXAMPLE
For n = 2, partition = (1, 1), the Symplectic Schur is: x_1*x_2 + x_1/x_2 + x_2/x_1 + 1/(x_1*x_2) + 1. There are five terms here. Partition (2) contributes another ten terms, including the term 1 twice. So a(2) = 5+10 = 15. [Extended by Andrey Zabolotskiy, Jan 24 2018]
MATHEMATICA
s[mu_, n_] := Expand[Simplify[Det[Table[x[j]^(mu[[i]]+n-i+1) - x[j]^(-mu[[j]]-n+i-1), {i, n}, {j, n}]] / Det[Table[x[j]^(n-i+1) - x[j]^(-n+i-1), {i, n}, {j, n}]]]];
Table[Sum[s[PadRight[mu, n], n] /. {x[_]->1}, {mu, IntegerPartitions[n]}], {n, 5}]
(* Andrey Zabolotskiy, Jan 24 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
T. Amdeberhan, Jul 13 2012
STATUS
approved