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A209664
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T(n,k) = count of degree k monomials in the power sum symmetric polynomials p(mu,k) summed over all partitions mu of n.
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10
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1, 2, 6, 3, 14, 39, 5, 34, 129, 356, 7, 74, 399, 1444, 4055, 11, 166, 1245, 5876, 20455, 57786, 15, 350, 3783, 23604, 102455, 347010, 983535, 22, 746, 11514, 94852, 513230, 2083902, 6887986, 19520264, 30, 1546, 34734, 379908, 2567230, 12505470, 48219486, 156167944, 441967518
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OFFSET
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1,2
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LINKS
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EXAMPLE
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Table starts as:
: 1;
: 2, 6;
: 3, 14, 39;
: 5, 34, 129, 356;
: 7, 74, 399, 1444, 4055;
: 11, 166, 1245, 5876, 20455, 57786;
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MAPLE
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b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
b(n, i-1, k) +`if`(i>n, 0, k*b(n-i, i, k))))
end:
T:= (n, k)-> b(n$2, k):
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MATHEMATICA
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p[n_Integer, v_] := Sum[Subscript[x, j]^n, {j, v}]; p[par_?PartitionQ, v_] := Times @@ (p[#, v] & /@ par); Table[Tr[(p[#, k] & /@ Partitions[l]) /. Subscript[x, _] -> 1], {l, 11}, {k, l}]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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