login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A082424 Coefficient of s(2n) in s(n,n) * s(n,n) * s(n,n) * s(n,n) * s(n,n) * s(n,n), where s(n,n) is the Schur function indexed by two parts of size n, s(2n) is the Schur function corresponding to the trivial representation and * represents the inner or Kronecker product. 3
1, 1, 11, 41, 320, 1917, 14582, 100562, 688427, 4380888, 26324611, 148136566, 785175771, 3925637781, 18586683128, 83578440418, 358079558873, 1465784048253, 5748270468573, 21649265291143, 78483868584001 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

I. G. Macdonald, Symmetric Functions and Hall Polynomials, Oxford Mathematical Monographs, Oxford Univ. Press, second edition, 1995.

LINKS

Table of n, a(n) for n=0..20.

FORMULA

a(n) = Sum_{gamma} Chi^{(n, n)}( gamma )^6/z(gamma) the sum is over all partitions gamma of 2n Chi^lambda(gamma) is the value of the symmetric group character z(gamma) is the size of the stablizer of the conjugacy class of symmetric group indexed by the partition gamma

MAPLE

compsclr := proc(k) local gamma; add( combinat[Chi]( [k, k], gamma)^6/ZEE(gamma), gamma= combinat[partition](2*k)); end: ZEE := proc (mu) local res, m, i; m := 1; res := convert(mu, `*`); for i from 2 to nops(mu) do if mu[i] <> mu[i-1] then m := 1 else m := m+1 fi; res := res*m; od; res; end:

CROSSREFS

Cf. A008763 change 6 to 4 in the above program.

Sequence in context: A201709 A092445 A068840 * A153173 A050526 A257967

Adjacent sequences:  A082421 A082422 A082423 * A082425 A082426 A082427

KEYWORD

nonn

AUTHOR

Mike Zabrocki, Apr 24 2003

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 25 22:28 EDT 2019. Contains 321477 sequences. (Running on oeis4.)