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.

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

Offset: 1

Author

Wouter Meeussen, Mar 11 2012

Keywords

• nonn
• tabl

Examples

			Table starts as:
:  1;
:  2,   6;
:  3,  14,   39;
:  5,  34,  129,  356;
:  7,  74,  399, 1444,  4055;
: 11, 166, 1245, 5876, 20455, 57786;
		

Links

• Alois P. Heinz, Rows n = 1..141, flattened
• Wikipedia, Symmetric Polynomials

Crossrefs

Main diagonal is A124577; row sums are A209665.

Programs

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}]