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 A209664 T(n,k) = count of degree k monomials in the power sum symmetric polynomials p(mu,k) summed over all partitions mu of n. 10
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Alois P. Heinz, Rows n = 1..141, flattened Wikipedia, Symmetric Polynomials EXAMPLE Table starts as: :  1; :  2,   6; :  3,  14,   39; :  5,  34,  129,  356; :  7,  74,  399, 1444,  4055; : 11, 166, 1245, 5876, 20455, 57786; MAPLE 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): seq(seq(T(n, k), k=1..n), n=1..10);  # Alois P. Heinz, Nov 24 2016 MATHEMATICA 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}] CROSSREFS Main diagonal is A124577; row sums are A209665. Sequence in context: A098810 A081469 A331441 * A072647 A100113 A300012 Adjacent sequences:  A209661 A209662 A209663 * A209665 A209666 A209667 KEYWORD nonn,tabl AUTHOR Wouter Meeussen, Mar 11 2012 STATUS approved

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Last modified August 7 04:39 EDT 2020. Contains 336274 sequences. (Running on oeis4.)