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Search: id:A082424
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| A082424 |
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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. |
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+0
4
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| 1, 1, 11, 41, 320, 1917, 14582, 100562, 688427, 4380888, 26324611, 148136566, 785175771, 3925637781, 18586683128, 83578440418, 358079558873, 1465784048253, 5748270468573, 21649265291143, 78483868584001
(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 )^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
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MAPLE
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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:
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CROSSREFS
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Cf. A008763 change 6 to 4 in the above program.
Sequence in context: A118572 A092445 A068840 this_sequence A153173 A050526 A104118
Adjacent sequences: A082421 A082422 A082423 this_sequence A082425 A082426 A082427
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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 24 2003
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