cp's OEIS Frontend

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.

%I A209664 #12 Nov 24 2016 17:36:26
%S A209664 1,2,6,3,14,39,5,34,129,356,7,74,399,1444,4055,11,166,1245,5876,20455,
%T A209664 57786,15,350,3783,23604,102455,347010,983535,22,746,11514,94852,
%U A209664 513230,2083902,6887986,19520264,30,1546,34734,379908,2567230,12505470,48219486,156167944,441967518
%N 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.
%H A209664 Alois P. Heinz, <a href="/A209664/b209664.txt">Rows n = 1..141, flattened</a>
%H A209664 Wikipedia, <a href="http://en.wikipedia.org/wiki/Symmetric_polynomials">Symmetric Polynomials</a>
%e A209664 Table starts as:
%e A209664 :  1;
%e A209664 :  2,   6;
%e A209664 :  3,  14,   39;
%e A209664 :  5,  34,  129,  356;
%e A209664 :  7,  74,  399, 1444,  4055;
%e A209664 : 11, 166, 1245, 5876, 20455, 57786;
%p A209664 b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A209664       b(n, i-1, k) +`if`(i>n, 0, k*b(n-i, i, k))))
%p A209664     end:
%p A209664 T:= (n, k)-> b(n$2, k):
%p A209664 seq(seq(T(n, k), k=1..n), n=1..10);  # _Alois P. Heinz_, Nov 24 2016
%t A209664 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 A209664 Main diagonal is A124577; row sums are A209665.
%K A209664 nonn,tabl
%O A209664 1,2
%A A209664 _Wouter Meeussen_, Mar 11 2012