A214043 Count of Laurent monomials (including multiplicities), in the Symplectic Schur symmetric polynomials s(mu, n) summed over all partitions mu of n.

2, 15, 134, 1589, 20162, 293580, 4519916, 75850054, 1334978228, 24987138510, 487322528552, 9968005618302, 211338028257280, 4658444968474433, 105985325960653194, 2492041019432287042, 60271996071301852442, 1500054086883728030496

Offset: 1

Author

T. Amdeberhan, Jul 13 2012

Keywords

• nonn

Examples

			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]
		

Links

• T. Amdeberhan, Theorems, problems and conjectures, arXiv:1207.4045 [math.RT], 2012-2015.

Programs

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 *)