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A090809
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Coefficient of the irreducible character of S_m indexed by (m-2n+2,2n-2) in the n-th Kronecker power of the representation indexed by (m-2,2).
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1
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0, 0, 2, 10, 31, 75, 155, 287, 490, 786, 1200, 1760, 2497, 3445, 4641, 6125, 7940, 10132, 12750, 15846, 19475, 23695, 28567, 34155, 40526, 47750, 55900, 65052, 75285, 86681, 99325, 113305, 128712, 145640, 164186, 184450, 206535, 230547
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OFFSET
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0,3
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COMMENTS
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REFERENCES
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A. Goupil, Combinatorics of the Kronecker products of irreducible representations of Sn, in preparation.
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LINKS
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FORMULA
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a(n) = 2*binomial(n, 2) + 4*binomial(n, 3) + 3*binomial(n, 4) = (n-1)*n*(3*n^2 + n + 10)/24.
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MAPLE
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f := proc(k) 2*binomial(k, 2)+4*binomial(k, 3)+3*binomial(k, 4); end;
seq (f(n), n=0..50);
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MATHEMATICA
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f[n_] := 2Binomial[n, 2] + 4Binomial[n, 3] + 3Binomial[n, 4]; Table[ f[n], {n, 0, 40}] (* Robert G. Wilson v, Feb 13 2004 *)
LinearRecurrence[{5, -10, 10, -5, 1}, {0, 0, 2, 10, 31}, 38] (* Jean-François Alcover, Sep 25 2017 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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