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A214043 Count of Laurent monomials (including multiplicities), in the Symplectic Schur symmetric polynomials s(mu, n) summed over all partitions mu of n. 0
2, 15, 134, 1589, 20162, 293580, 4519916, 75850054, 1334978228, 24987138510, 487322528552, 9968005618302, 211338028257280, 4658444968474433, 105985325960653194, 2492041019432287042, 60271996071301852442, 1500054086883728030496 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..18.

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

Sequence in context: A140306 A143924 A217483 * A215922 A285449 A288950

Adjacent sequences:  A214040 A214041 A214042 * A214044 A214045 A214046

KEYWORD

nonn

AUTHOR

T. Amdeberhan, Jul 13 2012

STATUS

approved

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Last modified October 23 17:49 EDT 2020. Contains 337969 sequences. (Running on oeis4.)