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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. 3
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 (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..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 * A039817 A293604 A000321

Adjacent sequences:  A082434 A082435 A082436 * A082438 A082439 A082440

KEYWORD

nonn

AUTHOR

Mike Zabrocki, Apr 25 2003

STATUS

approved

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Last modified March 19 23:02 EDT 2019. Contains 321343 sequences. (Running on oeis4.)