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.

1, 1, 11, 41, 320, 1917, 14582, 100562, 688427, 4380888, 26324611, 148136566, 785175771, 3925637781, 18586683128, 83578440418, 358079558873, 1465784048253, 5748270468573, 21649265291143, 78483868584001

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