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Search: id:A082437
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| A082437 |
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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. |
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+0
4
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| 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; listen)
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OFFSET
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0,3
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REFERENCES
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I. G. Macdonald, Symmetric Functions and Hall Polynomials, Oxford Mathematical Monographs, Oxford Univ. Press, second edition, 1995.
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FORMULA
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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
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MAPLE
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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:
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CROSSREFS
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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: A066833 A039813 A089515 this_sequence A039817 A000321 A039922
Adjacent sequences: A082434 A082435 A082436 this_sequence A082438 A082439 A082440
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KEYWORD
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nonn
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AUTHOR
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Mike Zabrocki (zabrocki(AT)mathstat.yorku.ca), Apr 25 2003
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