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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

%I

%S 1,2,6,3,14,39,5,34,129,356,7,74,399,1444,4055,11,166,1245,5876,20455,

%T 57786,15,350,3783,23604,102455,347010,983535,22,746,11514,94852,

%U 513230,2083902,6887986,19520264,30,1546,34734,379908,2567230,12505470,48219486,156167944,441967518

%N T(n,k) = count of degree k monomials in the power sum symmetric polynomials p(mu,k) summed over all partitions mu of n.

%H Alois P. Heinz, <a href="/A209664/b209664.txt">Rows n = 1..141, flattened</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Symmetric_polynomials">Symmetric Polynomials</a>

%e Table starts as:

%e : 1;

%e : 2, 6;

%e : 3, 14, 39;

%e : 5, 34, 129, 356;

%e : 7, 74, 399, 1444, 4055;

%e : 11, 166, 1245, 5876, 20455, 57786;

%p b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,

%p b(n, i-1, k) +`if`(i>n, 0, k*b(n-i, i, k))))

%p end:

%p T:= (n, k)-> b(n\$2, k):

%p seq(seq(T(n, k), k=1..n), n=1..10); # _Alois P. Heinz_, Nov 24 2016

%t 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}]

%Y Main diagonal is A124577; row sums are A209665.

%K nonn,tabl

%O 1,2

%A _Wouter Meeussen_, Mar 11 2012

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Last modified September 25 05:37 EDT 2020. Contains 337334 sequences. (Running on oeis4.)