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

1,2

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: A360006 A081469 A331441 * A360451 A072647 A100113

Adjacent sequences: A209661 A209662 A209663 * A209665 A209666 A209667

Keyword

nonn,tabl

Author

Wouter Meeussen, Mar 11 2012

Status

approved