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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
OFFSET
1,2
LINKS
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
KEYWORD
nonn,tabl
AUTHOR
Wouter Meeussen, Mar 11 2012
STATUS
approved