A082437 Coefficient of s(2n) in s(n,n) * s(n,n) * s(n,n) * s(n,n) * s(n,n), where s(2n) is the Schur function corresponding to the trivial representation, s(n,n) is a Schur function corresponding two the two row partition and * represents the inner or Kronecker product of symmetric functions.

1, 0, 5, 1, 36, 15, 228, 231, 1313, 1939, 6971, 11899, 33118, 59543, 140620, 254476, 538042, 959028, 1871808, 3258512, 5981444, 10140360, 17726166, 29257848, 49127549, 79032258, 128267727, 201437596

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..27.

Formula

a(n) = Sum_{gamma} Chi^{(n, n)}( gamma )^5/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)^5/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 for Chi( [k, k], gamma)^4/ZEE(gamma) instead of Chi( [k, k], gamma)^5/ZEE(gamma) in the programs above.

Sequence in context: A160632 A089515 A158820 * A308440 A039817 A293604

Adjacent sequences: A082434 A082435 A082436 * A082438 A082439 A082440

Keyword

nonn

Author

Mike Zabrocki, Apr 25 2003

Status

approved